Compaction property prediction of mixed gangue backfill materials using hybrid intelligence models: A new approach

Construction and Building Materials 247 (2020) 118633

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Compaction property prediction of mixed gangue backfill materials using hybrid intelligence models: A new approach Baiyi Li a,b, Hao Yan a,b,⇑, Jixiong Zhang a,b,⇑, Nan Zhou a,b a b

State Key Laboratory of Coal Resources and Safe Mining, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China School of Mines, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China

h i g h l i g h t s
A novel hybrid artificial intelligence model is proposed for predicting compaction property of MGBM.
SVM, DE and GWO algorithm are combined.
A large number of compaction tests using a self-made circular cylinder barrel are carried out.
The MIV method is used to investigate the relative importance of each input variable.

a r t i c l e

i n f o

Article history: Received 12 December 2019 Received in revised form 25 February 2020 Accepted 29 February 2020 Available online 6 March 2020 Keywords: Mixed gangue backfill materials Compaction property Support vector machines Differential evolution algorithm Gray wolf optimization algorithm Predictive model

a b s t r a c t Solid backfill coal mining has become one of the main means of green mining in coal mines because of its ability to control surface subsidence and disposal of surface gangue. Mixed gangue backfill material (MGBM) is the key factor for stratum control in solid backfill mining, and its compact mechanical performance directly affects the efficiency of backfill mining. In order to better carry out backfill mining design and backfill effect evaluation, a new hybrid artificial intelligence model integrating support vector machines (SVM), differential evolution algorithm (DE) and gray wolf optimization algorithm (GWO) is proposed to predict the compaction property of MGBM. The cement, lime and fly ash materials are selected to be mixed with gangue backfill materials and a large number of compaction tests using a self-made circular cylinder barrel are carried out to provide the dataset for the DGWO-SVM hybrid model. The input variables of this model include cement content, lime content, fly ash content and overburden stress, and the output variable of the model is the compaction property of MGBM. The performance of the DGWO-SVM model is evaluated by R2, MAE and RMSE. The predictive results indicate that the DGWO-SVM hybrid model can accurately predict the compaction property of MGBM, and the R2 of the training set and the testing set are 0.9518, 0.9137. Meanwhile, the relative importance of each input variable is implemented using the MIV method, and the importance scores of cement content, lime content, fly ash content and overburden stress are 0.3266, 0.0738, 0.2448, 0.3548, respectively. The research results can provide guidance for the optimization design of solid backfill mining. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction The large-scale exploitation of coal resources has caused serious damage to the mining environment. It can not only cause surface subsidence, destroy surface buildings, but also easily damage surface water and ground water, and cause air pollution [1,2]. At the same time, a large amount of gangue will be discharged in the

⇑ Corresponding authors at: State Key Laboratory of Coal Resources and Safe Mining, China University of Mining & Technology, Xuzhou, Jiangsu 221116, China. E-mail addresses: [email protected] (H. Yan), [email protected] (J. Zhang). https://doi.org/10.1016/j.conbuildmat.2020.118633 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

process of coal mining. In China, for example, more than 300 million tons of gangue are discharged each year. The accumulation of gangue on the ground will not only encroach the land, but also seriously pollute the groundwater and air [3,4]. Therefore, the use of solid waste such as gangue to fill the coal mine goaf, not only can effectively control surface subsidence, but also can dispose of waste gangue accumulated on the surface, which has become one of the important technical means to realize green mining of coal resources [5–7]. As the key factor for stratum control in solid backfill mining, the compact mechanical performance of solid backfill materials directly affects the efficiency of backfill mining [8,9]. At present,

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many research scholars have begun to study the mechanical properties of backfill materials, Li et al. analyzed the stress-strain relationship and stress-density relationship of gangue, aeolian sand, fly ash, loess and slag by compaction experiments, and derived the design formula for the weight ratio of backfill and mining [10]; Du et al. obtained the stress-strain curve of the unconfined compression backfilling structure by uniaxial compression experiments on a large cemented gangue backfill materials [11]; Cui et al. analyzed the influence of curing stress, initial temperature and drainage conditions on the mechanical properties of cemented tailings materials at early ages by laboratory tests [12]. It can be concluded that the current research on the mechanical properties of backfill materials is basically through laboratory tests. However, this method has some disadvantages such as long time consuming, complex testing process and expensive testing cost. In the design of backfill mining, the proportion optimization of mixed gangue backfill materials (MGBM) often needs to carry out a lot of experiments. Therefore, how to find other methods to study the compaction property of MGBM has caused more and more attention. At present, using non-destructive methods such as ultrasonic pulse velocity (UPV) and electrical resistivity (ER) tests is an effective way to predict the mechanical properties of backfill materials. As a non-destructive, low-cost, and less time-consuming method, previous researchers [13–15] suggested using UPV and ER tests instead of traditional uniaxial compression tests to predict the mechanical properties of backfill materials. Although it is very promising to use non-destructive methods to estimate the mechanical properties of backfill materials, a general correlation between the mechanical properties of backfill materials and the corresponding UPV values has not yet been established and it is difficult to cope with complex mining geological conditions. In recent years, artificial intelligence technology has been applied in all walks of life and has achieved significant development. Due to its unique advantages in dealing with complex nonlinearity, artificial intelligence technology can take into account all the factors affecting the process of backfill mining, thus achieving a better universal applicability and prediction effect [16,17]. At present, only a few researches used artificial intelligence to predict the mechanical properties of backfill materials, Orejarena and Fall used ANN to predict the strength of cemented paste backfill under sulfatetemperature coupling [18]; Qi et al. proposed a hybrid prediction model integrating BRT and PSO for predicting concrete strength [19]; Deng et al. established a 4-10-5 BP network model to predict cement backfill materials performance [20]. Although these research results have certain significance for the analysis of mechanical properties of backfill materials, there are at least three shortcomings in the above research: (1) the current research is all about predicting the strength of cemented paste backfill, and there is no prediction of the compaction performance of MGBM. The gangue particle size in MGBM is much larger than the particle size of the consolidated material (such as cement, lime, fly ash, etc.), and the main content of MGBM is gangue, it is different from the cemented paste backfill. Since the MGBM is not cemented into a complete body, it is impossible to analyze the unconfined compressive strength, so the confined compaction strength is studied by the self-made circular cylinder barrel in this paper; (2) the feasibility of other advanced artificial intelligence techniques, such as support vector machines (SVM), have not been used to predict the compaction property of MGBM; (3) although the grey wolf optimization algorithm (GWO) can be used to optimize SVM and achieve good optimization results [21], it is easy to fall into local optimum. Therefore, how to improve the optimization performance of GWO to optimize SVM has become a major problem. In view of this, a hybrid artificial intelligence model integrating SVM, differential evolution algorithm (DE) and GWO is proposed to predict the compaction property of MGBM. The cement, lime and

fly ash materials are selected to be mixed with gangue backfill materials and a large number of compaction tests using a selfmade circular cylinder barrel are carried out to provide the dataset for the DGWO-SVM hybrid model. The input variables of this model include cement content, lime content, fly ash content and overburden stress, and the output variable of the model is the compaction property of MGBM (i.e. strain value in the experiment). By training and testing DGWO-SVM model and comparing with GWOSVM and L-MRA prediction models, it shows that the proposed DGWO-SVM model has good prediction ability, and can effectively predict the compaction property of MGBM. 2. DGWO-SVM model In this paper, three artificial intelligence algorithms (including SVM, GWO, DE) are integrated to simulate the relationship between the compaction property of MGBM and its influencing variables. All three algorithms have been proved to have good prediction ability in nonlinear modeling, especially in materials science [22]. Each algorithm is briefly described below: 2.1. Support vector machines SVM is a learning algorithm with classification and regression functions developed based on statistical learning theory [23], the purpose of SVM is to use nonlinear mapping to transform input variables from low-dimensional space to high-dimensional space, thus transforming nonlinear problems into linear problems and finding linear relationships between input variables and output variables in high-dimensional space [24]. Assume the training set T = {(xi, yi)｜i = 1,2,3,  ,m}, and construct the regression function as y = wTU(x) + b, among them, U (x) is the nonlinear mapping function which can be used to map the original space to a high-dimensional space, then the optimization equation of SVM is as follows: m P min 12 k w k2 þ C ðni þ ni Þ i¼1 8 T > < yi  w  /ðxi Þ  b 6 e þ ni s:t:; wT  /ðxi Þ þ b  yi 6 e þ ni > : ni P 0; ni P 0

ð1Þ

where ni and ni* are slack variables; C is the penalty factor; and e is the loss function parameter. By introducing the Lagrange function in Eq. (1), the above optimization problem is transformed into the following equation by using the dual principle [25]:

"

max

 12

m P m P

 i Þð j 

ðai  a

i¼1 j¼1

s:t:;

m P i¼1

a

 j ÞKðxi ;xj Þ þ

a

m P i¼1

 i Þyi 

ðai  a

m P i¼1

#

ðai þ a

 iÞ

e

ðai  ai Þ ¼ 0;0 6 ai 6 C;0 6 ai 6 C ð2Þ

where ai is a Lagrangian multiplier and K(xi, yi) is a kernel function. In this paper, a Gaussian radial basis kernel function with good universality is used [26]. The function expression is:

  Kðxi ; xj Þ ¼ exp ck xi  xj k2

ð3Þ

where c is the kernel function parameter. In the above analysis, the penalty factor C controls the balance between the complexity of the training error and the prediction accuracy. The radial basis kernel function parameter c affects the speed of model training and prediction. Therefore, to construct a better prediction model, the internal parameters (C, c) of the

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SVM need to be optimized to determine the optimal combination of parameters. 2.2. Gray wolf optimization algorithm GWO is a group optimization algorithm that searches for the optimal value iteratively by simulating the hierarchical system and predation strategy of wolves [27]. As shown in Fig. 1, wolves in the grey wolf family can be divided into four categories according to their social status: a wolf, b wolf, d wolf and x wolf. When the gray wolf group is hunting, the hunting activity is dominated by the a wolf. The gray wolf group is rounded from all directions with the prey as the center. Under the leadership of the a wolf, the action is carried out by the b wolf and the d wolf closest to the prey. The x wolves fill the gap to prevent prey from escaping. The wolves repeatedly attacked and gradually narrowed the encirclement and eventually captured the prey [28]. In Fig. 1, Da, Db, and Dd respectively represent the distance between the current candidate gray wolf and the optimal three wolves, and the position of the candidate solution finally falls within the random circle position defined by a wolf, b wolf, and d wolf. In other words, the optimization process of the GWO algorithm is that the wolf groups increasingly close the gap between the high rank wolves and the prey. 2.3. DGWo As the gray wolf optimization algorithm is a swarm intelligence algorithm, its global optimization capability is weak. When faced with complex problems, it is easy to fall into local optimization, and it is hard to find the optimal solution from the global. Therefore, this paper introduces the differential strategy of the DE algorithm [29]. Through the mutation, crossover and selection process, the GWO algorithm can jump out of the local optimum, and make full use of the advantages of the DE algorithm in local optimization, and improve the optimization precision. The basic idea of DGWO is to divide the whole search process of the algorithm into two stages. In the first stage, the GWO search strategy embedded in the preferred operator is used to hunt for the optimal solution in the first 1/3 search process. If the optimal solution cannot be obtained, it goes to the second stage, that is, in the latter 2/3 search process, the differential evolution strategy of self-adjusting parameters is used to obtain the global optimal

3

solution, and at the same time, to ensure the evolution direction of the population, the greedy selection operator will be used to select whether to update the solution in both stages. The algorithm flow is shown in Fig. 2. 3. Experimental procedure In order to provide sufficient dataset for the DGWO-SVM hybrid model, a series of compaction tests of MGBM were carried out, the experimental procedures are as follows: 3.1. Materials In this paper, cement, lime and fly ash are selected to be mixed with gangue backfill materials to improve the compaction performance of gangue backfill materials. The gangue was taken from Yangzhuang coal mine in Huaibei, Anhui province; the cement was taken from P.O.42.5 cement; the lime was taken from Jiawang Lime Plant in Xuzhou, China; the fly ash was taken from the Yangzhuang coal mine power plant. The chemical compositions of gangue and three kinds of curing materials are measured in Table 1. It can be seen that the composition of SiO2 in gangue is the highest, which can serve as a skeleton for backfill materials during backfill mining, and improve the bearing capacity between gangue particles. Furthermore, the active Al2O3 and CaO in gangue can be reacted with cement, lime, and fly ash, to form products such as Ca (OH)2, hydrated calcium silicate and calcium hydrated aluminate [30]. As the hydration reaction continues, these hydration products are continuously formed and filled in the gaps between gangue particles, so that the backfill materials gradually solidify and harden, and the compaction performance of the backfill material is improved. 3.2. Sample preparation The original gangue taken from Yangzhuang coal mine was firstly crushed and sieved to obtain five kinds of gangue with particle sizes of 0–10 mm, 10–20 mm, 20–30 mm, 30–40 mm and 40– 50 mm, as shown in Fig. 3. According to the field application experience and the relevant backfill material particle size ratio study [31,32], the gangue samples were configured according to a certain mass ratio of the five different sizes.

Fig. 1. Gray wolf position update mechanism.

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Start GWO search

Update wolf position

Initialize parameters

DE search

Initialize the wolf individual position Xi Calculate objective of each particle Calculate objective of each search agent Update X

X

X

Set X as the best wolf N Set X as the second wolf Y Set X as the third wolf

Output optimal solution

Fig. 2. DGWO algorithm flow.

Table 1 Chemical compositions of gangue and three kinds of curing materials. Composition (%)

SiO2

Al2O3

CaO

Na2O

MgO

Fe2O3

SO3

Other elements

Gangue Cement Lime Fly ash

54.4 20.6 55.3 4.5

24.3 4.1 29.2 0.5

5.4 65.1 5.3 81.3

2.1 2.6 1.8 3.1

3.3 3.1 1.2 4.5

3.1 3.0 3.2 0.6

3.4 1.2 0.3 1.4

4.0 0.3 3.7 4.1

Fig. 3. The gangue samples after sieving.

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The cement, lime and fly ash are mixed into the abovementioned gangue samples based on the mix proportion shown in Table 2. During the preparation process, an appropriate amount of water is added, and the mixture is stirred and mixed into the MGBM. After the ingredients are completed, the mixture is allowed to stand for 6 h, and the mixture is initially consolidated, and then subjected to compaction test analysis.

experiment). The statistical characteristics for the entire dataset are shown in Table 3. For the DGWO-SVM model proposed in this paper, the entire dataset needs to be divided into the training dataset and the testing dataset according to a certain proportion [36,37]. In this study, the proportion of 7:3 is selected, that is, the training dataset consists of 224 samples, and the testing dataset consists of 96 samples.

3.3. Compaction test

4.2. Model establishment

The compaction mechanical properties test of MGBM were carried out under YAS-5000 rock mechanics test system with the maximum loading force of 5000kN. The compaction test is realized by the test system through a steel cylinder and a loading platen. In order to achieve confined compression conditions, a self-designed compacted steel cylinder is used as the holding device. The inner diameter of the steel cylinder is determined based on the maximum particle size of the test gangue (the inner diameter of the steel cylinder should not be less than 5 times the maximum gangue particle size), the wall thickness and material of the steel cylinder are determined by calculating the maximum tangential stress on the steel cylinder [3,33]. Therefore, the compacted steel cylinder has a cylindrical shape with an inner diameter of 250 mm, a cylinder depth of 305 mm, and a maximum charging height of 265 mm, as shown in Fig. 4. The compaction test of MGBM was carried out according to the loading speed of 1 kN/s, and the stress-strain curve during the compaction process was recorded. Fig. 5 shows the stress-strain relationship of the schemes S1, S3, S5, and S7. It can be seen that the mix proportion of MGBM has obvious influence on the compaction performance of the backfill materials. Thus, it is of great significance to study the compacting performance of MGBM under various conditions.

As shown in Fig. 6, this study proposes a hybrid artificial intelligence model integrating SVM, GWO, DE, namely DGWO-SVM, in which SVM is used to modelling the relationship between the compaction property of MGBM and its influencing variables, GWO and DE are used to optimize the hyper-parameters of the SVM (i.e. c and C). The parameters of the hybrid model are set as follows: the population size is 30, the maximum number of iterations is 100, and the crossover probability is 0.2. This study is divided into four steps to predict the compaction property of MGBM: (I) Dataset preparation; (II) Model establishment; (III) Model verification; (IV) Analysis of results. The first two steps have been explained in detail, and the latter two steps will be mainly described.

4. Methodology 4.1. Dataset preparation In this paper, the dataset used for the implementation of the DGWO-SVM model is derived from the MGBM compaction test. As mentioned above, a total of 16 sets of MGBM are carried out, the strain values of 1～20 MPa (interval 1 MPa) are recorded separately, that is, 20 sets of stress-strain values are recorded in each test scheme. Therefore, a total of 320 samples in dataset are used for training and testing. According to previous research experience [34–35], the dataset required for SVM-based model training and testing does not need to be very large. The 320 sets of data in this study can be used to effectively train and test the DGWO-SVM model. Based on the experimental scheme, the input variables of this model include cement content, lime content, fly ash content and overburden stress, and the output variable of the model is the compaction property of MGBM (i.e. strain value in the

4.3. Model verification Model verification is an important part of the model development process. The DGWO-SVM prediction model proposed in this paper needs to be fully verified before its application. In this paper, three performance indicators are selected to evaluate the relationship between the predictive and actual value, which include coefficient of determination (R2), root mean square error (RMSE) and mean absolute error (MAE). R2 represents the correlation degree between the predictive value and the measured value. The closer R2 is to 1, the better the correlation between the predictive value and the measured value. RMSE and MAE are two performance indicators of the error between the predictive value and the measured value. The smaller the RMSE and MAE values, the higher the prediction ability of the model. The three performance indicators can be expressed as follows:

Pn ðy  y Þ2 R2 ¼ 1  Pi¼1 i i 2 n i¼1 ðyi  yÞ RMSE ¼

MAE ¼

ð4Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ðy  yi Þ2 i¼1 i n

ð5Þ

 1 Xn   yi  yi  i¼1 n

ð6Þ

where n is the number of samples, yi* is the predictive value, yi is 

the measured value, y is the average of the measured values.

Table 2 Proportion scheme of mixed gangue backfill materials. Scheme

S1 S2 S3 S4 S5 S6 S7 S8

Curing material Cement content

Lime content

Fly ash content

20% 20% 20% 20% 30% 30% 30% 30%

5% 10% 15% 20% 5% 10% 15% 20%

5% 10% 15% 20% 10% 5% 20% 15%

Scheme

Curing material Cement content

Lime content

Fly ash content

S9 S10 S11 S12 S13 S14 S15 S16

40% 40% 40% 40% 50% 50% 50% 50%

5% 10% 15% 20% 5% 10% 15% 20%

20% 5% 10% 15% 20% 15% 10% 5%

Note: The content of each curing material is a percentage relative to the weight of gangue.

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Fig. 4. Test equipment: (a) schematic diagram; (b) the compaction system; (c) the steel cylinder.

5. Results and discussion 5.1. Performance of the DGWO-SVM hybrid model The DGWO-SVM hybrid model proposed in this study is trained and tested by the compaction test samples of MGBM. Fig. 7(a) shows the performance of the DGWO-SVM hybrid model on the training set. It can be found that the actual values and the predictive values of the training sample points are primarily distributed near the perfect fitting line. Meanwhile, it is also found that the predictive performance of sample point with larger strain value is better than that with smaller strain value, mainly because the sample point with smaller strain value is in the initial compaction stage of MGBM, and at this stage, the voids between the gangue particles are larger, the compaction deformation is larger, and the deformation process is more complicated. The R2 of the whole training dataset is 0.9518, which indicates that the training effect of the DGWO-SVM hybrid model is good. As shown in Fig. 7(b), the performance of the DGWO-SVM hybrid model on the testing dataset is also carried out. It shows that the actual values and the predictive values of the testing sample points are also primarily distributed near the perfect fitting line, and its R2 is 0.9137. No matter for testing set or training set, the predictive values of the DGWO-SVM model are close

Fig. 5. Stress-strain relationship of schemes S1, S3, S5, and S7.

Table 3 The statistical characteristics for the entire dataset. Variables

Min.

Max.

Mean

Unit

Variable

Cement content Lime content Fly ash content Overburden stress Compaction property of MGBM

20 5 5 1 0.0564

50 20 20 20 0.3633

35 12.5 12.5 10.5 0.2656

% % % MPa –

Input Input Input Input Output

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Fig. 6. Flowchart of the method in this study.

(a) training dataset

(b) testing dataset

Fig. 7. The performance of the DGWO-SVM hybrid model.

to the actual experimental values, which shows that the proposed DGWO-SVM hybrid model has good predictive ability, and is an effective tool to predict the compaction property of MGBM. 5.2. Comparative analysis of different predictive models In order to further reveal that the proposed predictive model has better forecasting ability, the DGWO-SVM hybrid model is compared with linear multivariate regression analyses (L-MRA) and GWO-SVM models. Among them, L-MRA belongs to traditional predictive model, and GWO-SVM and DGWO-SVM belong to artificial intelligence model. The training set is used to train the above 3 models, and the testing set is used to test the compaction property prediction performance. The results of comparative analysis are shown in Fig. 8 and Table 4. Fig. 8 shows the histogram of the experimental/predictive compaction property by different predictive models on testing set. It

can be seen that the mean value of the probability distribution cure of the three predictive models is basically distributed around 1. The mean values of L-MRA, GWO-SVM, and DGWO-SVM are 1.035, 1.022, and 1.006, respectively, which indicates that the predictive values of DGWO-SVM are closer to the experimental values. The comparison of evaluation indicators of different predictive models is shown in Table 4. From the aspect of R2, the R2 of DGWO-SVM is larger, its value is 0.9137, and the R2 of GWOSVM and L-MRA are only 0.8746, 0.8036; From the aspects of RMSE and MAE, the RMSE and MAE of DGWO-SVM are the smallest, the values are 0.0186 and 0.0148 respectively, while the RMSE and MAE of GWO-SVM and L-MRA are larger, which indicates that the prediction error of the DGWO-SVM hybrid model is smaller and the prediction accuracy is higher. At the same time, it can also be found that the predictive ability of the artificial intelligence model is significantly better than the traditional method. Therefore, the DGWO-SVM hybrid model is recommended to predict the compaction property of MGBM.

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(a) L-MRA

(b) GWO-SVM

(c) DGWO-SVM Fig. 8. Histogram of experimental/predictive compaction property using different predictive models on testing set.

Table 4 The comparison of evaluation indicators of different predictive models. Evaluation indicators

2

R RMSE MAE

Predictive model L-MRA

GWO-SVM

DGWO-SVM

0.8036 0.0250 0.0191

0.8746 0.0198 0.0148

0.9137 0.0186 0.0148

output results (Yj1 and Yj2). The difference between the two sets of results is called impact value (IV), and the average of all IVs is called MIV for each input variable. The MIV values are used to describe the sensitivity of each input parameter and the MIV values are calculated as follows:

   1 X n   MIV j ¼  ðY  Y j2 Þ  n i¼1 j1

ð7Þ

5.3. Relative importance of influencing variables According to the above analysis, cement content, lime content, fly ash content and overburden stress all have an impact on the compaction performance of MGBM. However, the influence degree of each input variable on the output results is unknown, and the sensitivity analysis of the influencing variables is needed. In this study, the mean impact value (MIV) is selected as an analytical tool to study the sensitivity of each input variable [38–40]. The basic idea is as follows: Firstly, the optimal DEGWO-SVM hybrid model is trained, and then each input variable Xj (j = 1, 2, 3, 4) of training set is increased by 10% and decreased by 10% (the remaining variables are kept unchanged), so two new input variables combinations (Xj1 and Xj2) of training set are obtained, that is, Xj1 = Xj  (1 + 10%), Xj2 = Xj(1–10%). In this manner, the DEGWO-SVM hybrid model is used to predict these two sets of

where n represents the number of samples, MIVj represents the MIV value of the j-th input variable. Fig. 9 shows the results of the importance analysis of each influencing variable. It can be found that the overburden stress has the most obvious impact on the compaction performance of MGBM, and its importance score reaches 0.3548, which indicates that the compaction performance of MGBM is fundamentally related to the stress, the requirement of MGBM is higher in the area with large stress environment. Meanwhile, the sensitivity of cement content and fly ash content on the compaction performance of MGBM ranks second and third, with the importance scores of 0.3266 and 0.2448, respectively, and the sensitivity of lime content is the lowest, with the importance score of 0.0738. Therefore, for different mine conditions, the overburden stress is different, thus the requirement for MGBM is different. Meanwhile, the mix

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CRediT authorship contribution statement Baiyi Li: Resources, Investigation, Software, Writing - original draft. Hao Yan: Methodology, Validation, Visualization, Writing review & editing. Jixiong Zhang: Conceptualization, Funding acquisition. Nan Zhou: Supervision, Project administration. Declaration of Competing Interest

Fig. 9. Importance score of each influencing variable.

proportion of cement and fly ash should be focused on in order to achieve a better backfill effect. The DEGWO-SVM hybrid model proposed in this study is a preliminary assessment tool for predicting the compaction performance of MGBM. In future, more field measured data or more indoor experiments will need to be monitored to enrich the dataset of the training samples. Never the less, due to the limited data available, only 4 variables are considered as input to the model for prediction, and more input variables, such as the creep characteristics of backfill materials, are needed to be considered in the future to train the model so that the predicted accuracy improves and generalization ability becomes better.

6. Conclusions In this study, a hybrid artificial intelligence model integrating SVM, GWO, DE, namely DGWO-SVM, is proposed, in which SVM is used to modelling the relationship between the compaction property of MGBM and its influencing variables, GWO and DE are used to optimize the hyper-parameters of SVM. The dataset used for the implementation of the DGWO-SVM model is derived from a large number of the MGBM compaction test. The input variables for the predictive model include cement content, lime content, fly ash content and overburden stress, and the output variable is the compaction property of MGBM (i.e. strain value in the experiment). A total of 320 sets of experimental data are collected to train and test the model, and R, RMSE and MAE are used to evaluate the performance of this prediction model. Furthermore, the model is compared with GWO-SVM and L-MRA models. Finally, the relative importance of each input variable is carried out by using the MIV method, and the main conclusions are as follows: (1) The proposed DGWO-SVM model can accurately predict the compaction property of MGBM, and DGWO is an efficient tool to optimize the hyper-parameters of SVM. The R2 of the training set in this model is 0.9518, and the R2 of the testing set is 0.9137, which shows that the DGWO-SVM hybrid model has good learning ability and predictive ability. (2) By comparing the L-MRA, GWO-SVM and DGWO-SVM models, it can be found that the prediction ability of the artificial intelligence model (DGWO-SVM, GWO-SVM) are better than the traditional prediction method (L-MRA), and the prediction accuracy of each model from high to low is: DGWOSVM, GWO-SVM, L-MRA. (3) The importance scores of cement content, lime content, fly ash content and overburden stress are 0.3266, 0.0738, 0.2448, and 0.3548, respectively. It indicates that the overburden stress, the cement content, and the fly ash content are all very sensitive variables, which should be considered when designing the MGBM.

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