Porosity Prediction of Granular Materials Through Discrete Element Method and Back Propagation Neural Network Algorithm

applied sciences

Article Porosity Prediction of Granular Materials through Discrete Element Method and Back Propagation Neural Network Algorithm

Yu Liu 1,*, Miaomiao Li 1 , Peifeng Su 1 , Biao Ma 1 and Zhanping You 2

1 School of Highway, Chang’an University, South Erhuan Middle Section, Xi’an City 710064, Shaan Xi Province, China; [email protected] (M.L.); [email protected] (P.S.); [email protected] (B.M.) 2 Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA; [email protected] * Correspondence: [email protected]

Received: 4 October 2019; Accepted: 26 February 2020; Published: 2 March 2020

Abstract: Granular materials are used directly or as the primary ingredients of the mixtures in industrial manufacturing, agricultural production and civil engineering. It has been a challenging task to compute the porosity of a granular material which contains a wide range of particle sizes or shapes. Against this background, this paper presents a newly developed method for the porosity prediction of granular materials through Discrete Element Modeling (DEM) and the Back Propagation Neural Network algorithm (BPNN). In DEM, ball elements were used to simulate particles in granular materials. According to the Chinese specifications, a total of 400 specimens in different gradations were built and compacted under the static pressure of 600 kPa. The porosity values of those specimens were recorded and applied to train the BPNN model. The primary parameters of the BPNN model were recommended for predicting the porosity of a granular material. Verification was performed by a self-designed experimental test and it was found that the prediction accuracy could reach 98%. Meanwhile, considering the influence of particle shape, a shape reduction factor was proposed to achieve the porosity reduction from sphere to real particle shape.

Keywords: Back Propagation Neural Network; highway engineering; Discrete Element Method; porosity prediction; granular materials; aggregate shape

1. Introduction Granular mixture is widely applied in industrial manufacturing, agricultural production and civil engineering, including powder metallurgy, food accumulation and building materials. For these mixtures, porosity is one of the most crucial factors that has a considerable impact on mixture structure and performance. However, due to the complex particle composition, it is hard to calculate or predict the mixture porosity without the help of lab experiments. In order to solve the above problems, many researchers have proposed different methods to calculate and analyze the porosity of granular mixtures. In particuology, packing density calculation models based on the packing theory were derived, including the Furnas model [1], linear packing density model [2], compressible packing model [3] and other improved models [4,5]. All of them are analytical models which were used to analyze particle spatial distributions and mixture packing densities. However, some literature [6,7] confirmed that these models were not accurate enough for complex problems and where particles have a wide range of sizes. A typical mixture in pavement engineering, however, is mainly composed of mineral aggregates with a wide range of particles sizes. The fine aggregates are less than 2.36 mm while the large particles can be larger than 19.0 mm.

Appl. Sci. 2020, 10, 1693; doi:10.3390/app10051693 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1693 2 of 19

Additionally, in pavement engineering, mixtures are formed through the lab or field compacting process which is dependent on the particle physical interactions. Evidently, these analytical models cannot consider the particle interactions during the compacting process. Based on the two considerations above, the authors believe that the conventional analytical models as discussed above are not applicable for predicting porosities of pavement mixtures. In pavement engineering, experimental testing methods were popularly used for studying mixture porosities [8,9]. In the past decades, many research studies were conducted for building the relationship between porosities and compositions of mixtures, while most of them were applied to specific projects or limited conditions [10,11]. Since 2005, with the rapid development of the discrete element methods (DEM), virtual mixture models have been developed for studying mix porosities [12,13], where particle gradations and morphological features were considered. With the DEM-based study, the researchers tended to explore the relations between the mix porosity and its mix composition. However, in the existing literature, the research purposes were mainly focused on evaluating a limited number of mixtures instead of finding a universal model for predicting mixture porosities [14,15]. In the past decades, machine learning algorithms have been widely used to solve problems which have multiple variables with no clear relations. Various models have been developed in industrial design [16], disease diagnosis [17], engineering analysis [18], material optimization [19–21], etc., which validated the high accuracy and the universal application of machine learning algorithms. Back Propagation Neural Network algorithm (BPNN), which is a multilayer feedforward neural network trained according to the error back propagation algorithm, is one of the most widely used algorithms. There are some advantages to this method: strong nonlinear mapping ability, highly self-learning and adaptive ability, good generalization ability and certain fault-tolerant ability. In recent years, some research efforts have been made in asphalt pavement engineering to study asphalt mixture’s volumetric properties, gradations and asphalt contents with the BPNN [20,22,23]. Additionally, the BPNN-based methods were also used for the prediction of cement concrete compression strength [24–26]. As demonstrated in the literature, the BPNN was useful and efficient in solving asphalt or concrete pavement problems. Obviously, the BP models have advantages for predicting mixture porosities. However, a reliable database which has enough data is one of the key requirements for using such a BP model. It is hard to obtain such a consistent database with the traditional experimental methods since their testing results are dependent on the testing methods, materials, specification and so on. One advantage of the DEM-based modeling approaches is lab-independent. First of all, with the DEM model, users can control one or a few key factors without effects from the other factors. For instance, it is possible to build a DEM model of mixture where all the particles have identical shapes if one wants to explore effects of gradations without influences of particle shapes. As a result, it is possible to obtain consistent results which stick to certain conditions. Secondly, limited by materials and testing conditions, it is very difficult to obtain a large amount of consistent experimental data. With the DEM model, however, it becomes possible to obtain a large amount of data as long as one has the DEM modeling techniques and computer facilities. Against the background discussed above, the main objectives of this research are to explore the prediction of granular materials’ porosities by combining the DEM simulation and the BPNN methods. The granular materials in this research refer to mineral aggregates whose sizes range from 2.36 mm to 19 mm. They are key constituents of asphalt mixtures which take over 90% of the overall mass and their porosities may significantly impact mixture volumetric and mechanical properties [27,28]. Compared to aggregates, asphalt acts more like lubricant during the compaction stage and its impact to mixture porosity can be ignored in this article [12,29]. According to the Chinese specifications, mixtures whose maximum particle sizes are from 13.2 mm to 19.0 mm are popularly used as high-quality pavement construction. As demonstrated in the previous research [13,30], both gradations and particle shapes could have certain impacts on mixture volumetric properties. When both gradations and particle shapes are considered simultaneously, it is not easy to make a consistent conclusion. Therefore, in this Appl. Sci. 2020, 10, 1693 3 of 19 article the aggregate gradations were selected as the major control parameters, while the particle shapes were considered as minor parameters by introducing a reduction factor.

2. Training Data Acquisition Based on Virtual Compacted Particle Mixtures

2.1. Coarse Aggregate Proportion Database

2.1.1. Determination of Possible Gradation Scope In order to contain all possible proportions of coarse aggregates from 2.36 mm to maximum particle size, the recommended range of each particle size group was summarized on the basis of Chinese Construction Specification JTG F40-2004 [31], including various common gradation types: asphalt concrete (AC), asphalt macadam (AM), open graded friction course (OGFC) and stone mastic asphalt (SMA). In this way, the maximum possible gradation scopes of different maximum nominal particle sizes are obtained finally, as shown in Tables1 and2.

Table 1. Possible gradation scope of Gradation-13.

Passing Rate (%) Sieving Size (mm) AC AM OGFC SMA Upper Limit Low Limit 13.2–16.0 90–100 90–100 90–100 90–100 100 90 9.5–13.2 68–85 50–80 60–80 50–75 85 50 4.75–9.5 38–68 20–45 12–30 20–34 68 12 2.36–4.75 24–50 8–28 10–22 15–26 50 8

Table 2. Possible gradation scope of Gradation-16.

Passing Rate (%) Sieving Size (mm) AC AM OGFC SMA Upper Limit Low Limit 16.0–19.0 90–100 90–100 90–100 90–100 100 90 13.2–16.0 76–92 60–85 70–90 65–85 96 60 9.5–13.2 60–80 45–68 45–70 45–65 83 45 4.75–9.5 34–62 18–40 12–30 20–32 62 12 2.36–4.75 20–48 6–25 10–22 15–24 48 6

It could be observed that the mineral mixtures had a large particle size polydispersity, but the particle size ratios in each sieving size group in pavement materials were relatively small. However, the particle size distribution of the mixture can be adjusted by changing the proportion of sieving groups.

2.1.2. Establishment of Coarse Aggregate Proportion Database Machine learning algorithms require large sample size to ensure the stability and accuracy or prediction results. In order to obtain enough test data for training for both Gradation-13 and Gradation-16, 200 coarse aggregates’ proportions were randomly created by VBA within the upper and lower limit listed in Tables1 and2. As shown in Figures1 and2, 200 combinations cover almost all possible gradations between upper and lower limit for one gradation type. Appl. Sci. 2020, 10, 1693 4 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 19

Figure 1. 200 coarse aggregate proportions of Gradation-13. FigureFigure 1. 1. 200200 coarse coarse aggregate aggregate proportions proportions of of Gradation Gradation-13.-13.

FigureFigure 2. 2. 200200 coarse coarse aggregate aggregate proportions proportions of of Gradation Gradation-16.-16. Figure 2. 200 coarse aggregate proportions of Gradation-16. InIn the the above above two two figures figures,, the the upper upper and and lower lower rough rough lines lines represent represent the the upper upper and and lower lower bounds bounds In the above two figures, the upper and lower rough lines represent the upper and lower bounds ofof the gradation.gradation. Meanwhile,Meanwhile, each each fine fine line line in thein the middle middle of upper of upper and lowerand lower limits limits represents represents a particle a of the gradation. Meanwhile, each fine line in the middle of upper and lower limits represents a particlecombination. combination. Although Although particle particle compositions compositions cannot cannot be listed be listed completely, completely, figures figure justifys justify that that the particle combination. Although particle compositions cannot be listed completely, figures justify that thesamples samples used used for for model model training training are are representative. representative. the samples used for model training are representative. 2.2. Virtual Compacted Model Design 2.2. Virtual Compacted Model Design In this study, Particle Flow Code (PFC) was applied to carry out the virtual compaction test. In this study, Particle Flow Code (PFC) was applied to carry out the virtual compaction test. Static compaction, as a commonly used compaction method in road material’s DEM modelling, was Static compaction, as a commonly used compaction method in road material’s DEM modelling, was chosen, considering both compacting effect and computing efficiency. In addition, in order to chosen, considering both compacting effect and computing efficiency. In addition, in order to Appl. Sci. 2020, 10, 1693 5 of 19

2.2. Virtual Compacted Model Design

Appl. Sci.In this2020,study, 10, x FOR Particle PEER REVIEW Flow Code (PFC) was applied to carry out the virtual compaction test.5 Static of 19 compaction, as a commonly used compaction method in road material’s DEM modelling, was chosen, determineconsidering a both suitable compacting static compaction effect and pressure, computing the e ffi influenceciency. In of addition, static pressure in order applied to determine for the compactiona suitable static was compactiontested in detail. pressure, It should the be influence noted that of static all particles pressure are applied ball shape for thed in compactionorder to control was atested single in variable detail. It in should this stage. be noted Three that gradations all particles were are selected ball shaped randomly in order and to control their passing a single rates variable are shownin this stage.in Table Three 3. gradations were selected randomly and their passing rates are shown in Table3.

TableTable 3. Passing rates of three gradations for static pressure test.test.

SievingSieving Sizes Sizes (mm) (mm) 19.019.0 16.016.0 13.2 13.2 9.59.5 4.75 4.752.36 2.36 Gradation#1Gradation#1 100100 9191 72 72 69 6956 5639 39 PassingPassing Rate Rate (%) (%) Gradation#2Gradation#2 100100 9292 62 62 57 5730 3022 22 Gradation#3Gradation#3 100100 9393 91 91 77 7720 2019 19

Since all the particle combinations were were a coarse part of an entire gradation, the total mass of differentdiﬀerent mixtures may also be different. diﬀerent. All elements were generated in accordance accordance with passing rate and total volumevolume ofof design design specimen. specimen. The The boundary boundary condition condition for for the the container container is simulated is simulated by a by wall, a wallwhich, which is similar is similar to its to counterpart its counterpart steel containersteel container in the in laboratory the laboratory test. Thetest. compactionThe compaction pressure pressure only onlyapplied applied on top on and top bottom and bottom wall. Thewall. height The height of design of cylindricaldesign cylindrical specimen specimen is 100 mm is and100 mm the diameter and the diameterof the container of the container is also 100 is mm. also 100 mm. For each specim specimen,en, the virtual test mainly follows three steps: (1) TheThe ball ball elements elements were were generated generated without without overlap overlap in in a a random random position position in in a a cylindrical area; (2) SevenSeven levels levels of hydrostatichydrostatic pressure pressure were were applied applied to to compact compact seven seven specimens, specimens, including including 100 kPa,100 kPa,200 kPa,200 kPa, 300 kPa,300 kPa, 400 kPa,400 kPa, 500 kPa,500 kPa, 600 kPa600 andkPa 700and kPa;700 kPa; (3) Compression was performed until all elements become stable as shown in Figure 3. At that time, (3) Compression was performed until all elements become stable as shown in Figure3. At that time, mixtures are considered to be in the most compact state. mixtures are considered to be in the most compact state.

Static Compression

Figure 3. Virtual compression model. Figure 3. Virtual compression model. Because there are only coarse aggregates in this model, linear contact model was applied to all particles.Because The there density are of only aggregates coarse aggregates was set as 2650 in this g/cm model,3 and elinearﬀective contact modulus model and was friction applied coeﬃ tocient all 3 particles.were 50 GPa The and density 0.4, respectively. of aggregates The wasresults set are as shown 2650 g/cm in Table and4. effective modulus and friction coefficient were 50 GPa and 0.4, respectively. The results are shown in Table 4.

Appl. Sci. 2020, 10, 1693 6 of 19

Table 4. The mixture porosity of diﬀerent compaction pressures.

Compaction Pressure (kPa) 100 200 300 400 500 600 700 Gradation#1 0.334 0.334 0.332 0.330 0.329 0.329 0.328 Mixture Porosity Gradation#2 0.363 0.366 0.361 0.359 0.357 0.354 0.354 Gradation#3 0.401 0.401 0.401 0.400 0.398 0.396 0.394

It can be observed that compaction pressure caused little effect on final porosity for same gradation mixture. Taking Gradation#1 as an example, the range of mixture porosity is from 0.328 to 0.334, which indicates the mixture with sphere particles can be well compacted at all above pressures. Meanwhile, a compaction pressure of 600 kPa is commonly used in laboratory tests in many countries’ specification, for instance, Superior Performing Asphalt Pavement (SUPERPAVE) specification. Therefore, a fixed compaction pressure of 600 kPa was chosen to carry out virtual compaction tests in this study. The particle number in each specimen varies from about 1000 to 17,000 for different gradations, and computing time changes from 10 min to nearly 2 h.

2.3. Data Recording Through above virtual compaction models, the porosity of coarse aggregates (larger than 2.36 mm) mixtures were measured and recorded. In order to eliminate the impact of contingency, three gradations were randomly selected and ﬁve parallel virtual experiments were conducted. In each group of parallel virtual experiments, the particle size distributions were identical, but the initial positions of ball elements were diﬀerent. The detailed results are shown in Table5.

Table 5. Recorded porosity of parallel specimens.

Test Number Gradation#1 Gradation#2 Gradation#3 1 0.3885 0.3778 0.3516 2 0.3932 0.3781 0.3516 3 0.3934 0.3759 0.3524 4 0.3908 0.3816 0.3519 5 0.3895 0.3785 0.3527 Mean value 0.3911 0.3784 0.3520 Variance 0.0019 0.0018 0.0004

According to the results, it can be observed, that for the same gradation, the porosity measured by different parallel specimens is very close. However, there are great differences among different gradations, which shows that the results of the virtual compaction test were credible. Therefore, the porosity of Gradation-13 and Gradation-16 specimens were recorded respectively in the same way. The following Tables6 and7 show the final results of two types of gradation. Appl. Sci. 2020, 10, 1693 7 of 19

Table 6. Recorded data of Gradation-13.

Independent Variable X-Retained Percentage of Each Particle Specimen Size Group Dependent Variable Y-Porosity 13.2–16.0 mm 9.5–13.2 mm 4.75–9.5 mm 2.36–4.75 mm #1 0.06 0.3 0.16 0.33 0.3408 #2 0.06 0.25 0.12 0.27 0.3406 #3 0.06 0.27 0.43 0.07 0.3760 #4 0.06 0.21 0.12 0.38 0.3462 #5 0.07 0.33 0.41 0.06 0.3795 ...... #196 0.01 0.4 0.35 0.05 0.3863 #197 0.04 0.19 0.23 0.34 0.3507 #198 0.01 0.15 0.21 0.18 0.3560 #199 0.04 0.2 0.23 0.07 0.3719 #200 0.02 0.15 0.28 0.11 0.3642

Table 7. Recorded data of Gradation-16.

Independent Variable X-Retained Percentage of Each Particle Size Group Dependent Specimen 16.0–19.0 mm 13.2–16.0 mm 9.5–13.2 mm 4.75–9.5 mm 2.36–4.75 mm Variable Y-Porosity #1 0.01 0.04 0.48 0.17 0 0.4149 #2 0.06 0.05 0.16 0.36 0 0.4020 #3 0.02 0.06 0.39 0.37 0.01 0.3966 #4 0.07 0.02 0.14 0.57 0.01 0.3993 #5 0.05 0.09 0.12 0.6 0.01 0.3946 ...... #196 0.08 0.19 0.04 0.08 0.44 0.3365 #197 0.07 0.1 0.2 0.12 0.44 0.3372 #198 0.06 0.11 0.21 0.03 0.48 0.3379 #199 0.02 0.26 0.13 0.01 0.5 0.3342 #200 0.03 0.27 0.08 0.03 0.51 0.3364

Based on above data, the internal relationship between independent variables (retained percentage of each particle size group) and dependent variable (porosity) will be further analyzed in the next chapter.

3. Data analysis and BP Neural Network Model Building MATLAB software included plenty of useful functions of neural network algorithm in the Neural Network Toolbox as shown in the literature [32]. These functions provide the possibility to build a basic model for those not professional at machine learning. Therefore, the BPNN models in this article were built with “newﬀ” function in Neural Network Toolbox of MATLAB, which is easy for reference. In general, the BP neural network model includes an input layer, an output layer and multiple hidden layers. The previous research shows that the three layer BP neural network with one hidden layer can approximate any non-linear function [32]. Hence, the model in this article was established with one hidden layer and the model structure is shown in Figure4. Appl. Sci. 2020, 10, 1693 8 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 19

Figure 4. BP neural network model structure. Figure 4. BP neural network model structure. In the BP model, there are three kinds of key parameters: (1) input and output variables; (2) transfer In the BP model, there are three kinds of key parameters: (1) input and output variables; (2) function; (3) the number of hidden layer nodes and their corresponding weight thresholds. Through transfer function; (3) the number of hidden layer nodes and their corresponding weight thresholds. the above three parameters, a complete BP neural network prediction model can be obtained and Through the above three parameters, a complete BP neural network prediction model can be obtained calculated through Equation (1). and calculated through Equation (1). Xn푛 Xmm T = Vi( f (WkiXk + εi) + η) (1) T = ∑ 푉푖(∑ 푓(푊푘푖푋푘 + 휀푖) + η) (1) i=1 k=1 푖=1 푘=1 wherewhere (1) (1)X k푋represents푘 represents model model input input variables variables (particle (particle volume volume fraction fraction of different of different particle sizeparticle groups); size Tgroups);represents T represents model output model result; output k representsresult; k represent the numbers the number of input of variables input variables in the range in the of range 1 to m; of m1 to represents m; m represents the total the number total number of input of input variables, variables, four forfour Gradation-13 for Gradation and-13 and five five for for Gradation-16; Gradation- (2)16;f ((2)x) refersf(x) refers to transfer to transfer function; function; (3) i represents (3) i represent the numbers the number of hidden of hidden layer nodes layer innodes the rangein the of range 1 to nof; n 1refers to n; n to refers the total to the number total number of hidden of layerhidden nodes; layerW nodeki representss; 푊푘푖 represents weight from weight input from layer input to hidden layer layer;to hiddenVi refers layer; to 푉 weight푖 refers from to weight hidden from layer hidden to output layer layer; to outputεi represents layer; threshold휀푖 represent froms threshold input layer from to hiddeninput layer layer; toη hiddenrepresents layer; threshold η represent froms threshold hidden layer from to hidden output layer layer. to output layer. InIn addition, addition, in in order order to evaluate to evaluate model model training training accuracy, accuracy, Mean Square Mean Error Square (MSE) Error and (MSE) coefficient and ofcoefficient determination of determination (R2) of the output(푅2 ) of results the output are applied results and are MSE applied can and be calculated MSE can be according calculated to Equationaccording (2). to Equation (2). n 1 X푛 2 MSE = 1 (Ti ti) (2) MSE =n ∑(푇 − 푡 )2 (2) 푛 i=1 푖 푖 푖=1 where Ti represents the test value and ti represents the real value. Meanwhile, n refers to the test set samplewhere 푇 number.푖 represents the test value and 푡푖 represents the real value. Meanwhile, n refers to the test set sampleIn “new number.ff” function, there are not too many parameters to be determined. Hence, all of them are listedIn in “newff” the following function, Table there8. are not too many parameters to be determined. Hence, all of them are listed in the following Table 8. Table 8. Parameters needed in “newff” function. Table 8. Parameters needed in “newff” function. Parameters Value/Function Parameters Value/Function net_bp.trainParam.epochs 100 net_bp.trainParam.epochs 1006 net_bp.trainParam.goal 1 10− ; × −6 net_bp.trainParam.shownet_bp.trainParam.goal 1 10× 10 ; net_bp.trainParam.shownet_bp.trainParam.lr 0.00110 Numbernet_bp.trainParam.lr of neuron nodes Gradation-13:4;0.001 Gradation-16:5 NumberTF (Transfer of neuron function) nodes tansigG (hiddenradation layer);-13:4; purelin Gradation (output-16:5 layer) BTF (Backprop network training function) trainlm BLF (BackpropTF weight(Transfer/bias function) learning function_ tansig (hidden layer); learngdm purelin (output layer) BTF (BackpropPF (Performance network function) training function) MSE (Meantrainlm Square Error) BLF (Backprop weight/bias learning function_ learngdm PF (Performance function) MSE (Mean Square Error) Appl. Sci. 2020, 10, 1693 9 of 19

Because of the high relativity between gradation and mixture porosity, the prediction accuracy was great enough when the default functions were applied. In order to simplify the procedures of building the prediction model, the default transfer functions were ﬁnally determined. It should be noted that the determination of other key parameters is illustrated in the following Chapter 3.1, Input and output variables processing.

3.1. Input and Output Variables Processing For the model in this article, the input layer contains four variables (i.e., particle volume fraction of 13.2–16.0 mm, 9.5–13.2 mm, 4.75–9.5 mm and 2.36–4.75 mm) for Gradation-13 and ﬁve variables for Gradation-16, and output layer includes the only dependent variable, porosity, for both gradation types. The ﬁrst and foremost step in BP neural network modeling is to process the original input data. Because the recorded data are relatively close to each other in the whole range of 0.30–0.45, it is necessary to standardize the original data and transfer variables into the range of [–1, 1] according to Equation (3). Meanwhile, the original gradation should also be processed through Equation (3). This procedure can achieve the best performance for modeling.

(ymax ymin) (x0 xmin) y0 = − × − + ymin (3) (xmax x ) − min where ymax and y represent 1 and 1 respectively in this article, while xmax and x refer to the min − min maximum and minimum value of recorded porosity and x0 refers to original porosity, while y0 refers to standardized porosity. Through the above equation, the procedure for standardizing the input variables includes these three parts: (1) ﬁnding maximum and minimum values in the recorded porosity as xmax and xmin; (2) calculating each standardized porosity (y0) value through Equation (3); (3) recording standardized porosity (y0) values. The next step is to divide the available data set into two groups, one for training and another for testing the developed model. Meanwhile, the testing set will not be used in the model training process. It should be noted that grouping is done randomly. In this study, 200 particle compositions and corresponding porosity for both Gradation-13 and Gradation-16 were randomly divided into training and testing groups. Finally, the output results still need to be anti-standardized in a similar way by following Equation (4): (xmax xmin) (y1 ymin) x1 = − × − + xmin (4) ymax y − min where, xmax and xmin refer to the maximum and minimum value of recorded porosity and x1 refers to prediction porosity, while y1 refers to standardized prediction porosity. The standardized and anti-standardized can be completed automatically by function “mapminmax” in MATLAB only if the original data is inputted.

3.2. Transfer Function Determination There are three transfer functions commonly used in the BP neural network model and these functions are applied in the hidden and output layer. The default transfer functions in “newﬀ” function include a hyperbolic tangent function(“tansig”) in hidden layer as shown in Equation (5) and a pure linear function(“purelin”) in the output layer in Equation (6).

2 tan sig(n) = (5) 2n 1 (1 + e− )−

purelin(n) = n (6) Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 19

Appl. Sci. 2020, 10, 1693 10 of 19 The final prediction formula can be obtained by training the model to determine the appropriate parameters. Among these parameters, the number of hidden layer nodes should be tested by user. TheThe other ﬁnal corresponding prediction formula parameters can be could obtained be determined by training automatically. the model to determine the appropriate parameters. Among these parameters, the number of hidden layer nodes should be tested by user. The3.3. other Hidden corresponding Layer Node Number parameters Determination could be determined automatically.

3.3. HiddenGenerally, Layer Node the Numbermodel accuracy Determination will be improved by increasing the training sample size. However, when the sample size is large enough, even more data cannot improve the model performance.Generally, theFor modelthe purpose accuracy of studying will be improved the relationship by increasing between the original training sample sample size size. and However, training whenmodel the performance, sample size is different large enough, training even sample more data sizes cannot were improve tested and the comodelmpared. performance. The mean For square the purposeerror (MSE) of studying and coefficient the relationship of determination between original (R2) between sample prediction size and training value and model virtual performance, test value diwerefferent calculated training sample to evaluate sizes werethe accuracy tested and and compared. stability Theof final mean prediction square error model. (MSE) Seven and coemodelsfficient for 2 ofGradation determination-13 were (R ) built between in this prediction article value with sample and virtual sizes test of value 25, 50, were 75, calculated 100, 125, to150 evaluate and 175 therespectively. accuracy and For stability all seven of models, final prediction 25 samples model. were applied Seven models as the testing for Gradation-13 group to check were the built model in thisperformance article with by sample calculating sizes R of2. 25, 50, 75, 100, 125, 150 and 175 respectively. For all seven models, 2 25 samplesFor the were BP applied model, asexcept the testing for training group sample to check size, the modelthe hidden performance layer node by calculatingnumber also R plays. a significantFor the role BP model, in model except training. for trainingAccording sample to empirical size, the Equation hidden layer(7), the node range number of node also number plays is a significantset as 3 to 13. role in model training. According to empirical Equation (7), the range of node number is set as 3 to 13. h =h =√m√푚++n 푛++a 푎 (7)(7) where, m and n refer to the number of input and output layer nodes respectively and a refers to a where, m and n refer to the number of input and output layer nodes respectively and a refers to regulating constant in the range of 1 to 10. For each group, 10 parallel tests were carried out to a regulating constant in the range of 1 to 10. For each group, 10 parallel tests were carried out to determine the optimum node number. The detailed procedure is omitted in this article since it was determine the optimum node number. The detailed procedure is omitted in this article since it was introduced in another publication [32]. The following Figure 5 shows that coefficient of determination introduced in another publication [32]. The following Figure5 shows that coe fficient of determination (R2) changes with node number. (R2) changes with node number.

Figure 5. R2 in different node numbers and training group sizes. Figure 5. R2 in different node numbers and training group sizes. It can be observed that: (1) the optimum node number can be different for different models; (2) with trainingIt can be sample observed sizeincreasing, that: (1) the model optimum performance node number is less sensitivecan be different to node for number. different The models; optimum (2) hiddenwith training layer node sample number size for increasing, all seven groups model are performance shown in the is following less sensitive Table to9. node number. The optimum hidden layer node number for all seven groups are shown in the following Table 9. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 19

Appl. Sci. 2020Table, 10 9., 1693 The optimum node number, corresponding R2 and mean square error (MSE) of different11 of 19 training group sizes.

TrainingTable 9. The Group optimum Sizes node Optimum number, correspondingNode Number R 2 andMean mean Value square of R error2 Mean (MSE) Value of diﬀerent of MSE training group25 sizes. 4 0.837615 0.073948 Training Group50 Sizes Optimum Node4 Number Mean0.954905 Value of R2 Mean Value0.012391 of MSE 75 7 0.977096 0.007002 25 4 0.837615 0.073948 50100 45 0.9549050.98425 0.0123910.00472 75125 78 0.9770960.983784 0.0070020.004031 100150 55 0.984250.988016 0.004720.002924 125175 812 0.9837840.988349 0.0040310.003112 150 5 0.988016 0.002924 175 12 0.988349 0.003112 Meanwhile, the following Figure 6 shows the R2 for different models based on their optimum node number. The error bars here represent standard deviation. Meanwhile, the following Figure6 shows the R 2 for diﬀerent models based on their optimum node number. The error bars here represent standard deviation.

Figure 6. R2 for diﬀerent training group sizes.

2 From this ﬁgure, it is clearFigure that with 6. R the for increasedifferent training of training group group sizes. sizes, R2 rises sharply in the initial stage. After the number of training groups goes up to more than 75, the growth rate of R2 From this figure, it is clear that with the increase of training group sizes, R2 rises sharply in the becomes very small. Meanwhile, for model accuracy, when the amount of training data is too small, initial stage. After the number of training groups goes up to more than 75, the growth rate of R2 the model error is very large. With the increase of training data size, the model tends to be more stable. becomes very small. Meanwhile, for model accuracy, when the amount of training data is too small, In this state, a more accurate prediction model can be obtained. the model error is very large. With the increase of training data size, the model tends to be more Based on the above analysis, the number of training sets was recommended as 75 or 100, stable. In this state, a more accurate prediction model can be obtained. considering training accuracy and eﬃciency. Meanwhile, the best number of testing sets is about Based on the above analysis, the number of training sets was recommended as 75 or 100, 1/2–1/3 of the training set. considering training accuracy and efficiency. Meanwhile, the best number of testing sets is about 1/2– 3.4.1/3 Testing of the Resultstraining set.

3.4.On Testing the basis Results of the existing database, 150 groups were used as the training group and 50 groups were applied as the testing group to build the BP neural network model. The training results are shown in Figure7 for Gradation-13 and Figure8 for Gradation-16. In the process of data transmission, through repeated training, four hidden layer nodes for Gradation-13 and ﬁve nodes for Gradation-16 were ﬁnally determined as the most suitable number of hidden layer nodes. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 19

On the basis of the existing database, 150 groups were used as the training group and 50 groups were applied as the testing group to build the BP neural network model. The training results are shown in Figure 7 for Gradation-13 and Figure 8 for Gradation-16. In the process of data transmission, through repeated training, four hidden layer nodes for Gradation-13 and five nodes for Gradation-16 were finally determined as the most suitable number Appl. Sci. 2020, 10, 1693 12 of 19 of hidden layer nodes.

Figure 7. Porosity c comparisonomparison among testing value and predicted value for Gradation-13.Gradation-13.

Figure 8. Porosity comparison among testing value and predicted value for Gradation-16. Figure 8. Porosity comparison among testing value and predicted value for Gradation-16. For two models, their coeﬃcients of determination both achieve 99%, which means porosity For two models, their coefficients of determination both achieve 99%, which means porosity prediction models have enough accuracy to provide reliable results. prediction models have enough accuracy to provide reliable results. In addition, all the related parameters applied in model training are listed in the following tables. In addition, all the related parameters applied in model training are listed in the following tables. Tables 10 and 11 provide the gradation and porosity normalization parameters (xmax, xmin, ymax, ymin) Tables 10 and 11 provide the gradation and porosity normalization parameters for Gradation-13 and Gradation-16. Through these parameters, the original gradation and porosity (풙풎풂풙, 풙풎풊풏, 풚풎풂풙, 풚풎풊풏) for Gradation-13 and Gradation-16. Through these parameters, the original data풎풂풙 could풎풊풏 be풎풂풙 normalized풎풊풏 according to Equation (3). Then, the weights and thresholds used to transfer data from the input layer to the hidden layer are shown in Table 12, while those parameters from the hidden layer to the output layer are shown in Table 13. Appl. Sci. 2020, 10, 1693 13 of 19

Table 10. The gradation normalization parameters for Gradation-13 and Gradation-16.

Type xmax xmin ymax ymin

Gradation-13 0.10 0.46 0.68 0.47 0.01 0.07 0.01 0.01 1 1 − Gradation-16 0.10 0.36 0.44 0.61 0.51 0.01 0 0.01 0 0 1 1 −

Table 11. The porosity normalization parameters for Gradation-13 and Gradation-16.

Type xmax xmin ymax ymin Gradation-13 0.4075 0.3311 1 1 − Gradation-16 0.4052 0.3200 1 1 −

Table 12. The parameters from the input layer to hidden layer for Gradation-13 and Gradation-16.

Type Weight 1 Threshold 1 − − 0.4316 0.2161 1.2462 1.3345 2.7932 − − − − 0.0450 0.1616 0.8563 0.8893 0.3971 Gradation-13 − − − 0.3822 0.8933 0.2511 1.0650 0.8875 − 0.0969 0.0735 0.6174 2.5105 2.6779

0.0245 0.0011 0.0336 0.7609 2.9034 3.4968 − − − − 0.0735 0.0087 0.1996 1.2099 1.3825 1.6782 − − Gradation-16 0.2572 0.7488 0.5424 0.4109 0.5989 0.3126 − − 0.0813 0.2895 0.4094 0.1188 1.8452 0.9682 − − − − 0.3841 0.2343 1.0723 0.8142 1.3661 1.1031 − − − −

Table 13. The parameters from the hidden layer to output layer for Gradation-13 and Gradation-16.

Type Weight 2 Threshold 2 − − Gradation-13 0.1552 0.7475 0.4340 0.9771 1.1815 − − − − Gradation-16 2.0664 0.4469 0.4462 0.7392 0.0103 1.7224 − − −

The complete prediction calculation process is listed as follows:

Step1: Original gradation and porosity data are recorded and inputted to MATLAB program. Step2: All the original data are normalized according to Equation (3) and parameters in Tables 10 and 11. Step3: The values in hidden layer are calculated according to Equations (8).

Hidden layer value = tansig(Weight 1 normalized input data + Threshold 1) (8) − × − Step4: The values in output layer are calculated according to Equations (9).

Output layer value = purelin(Weight 2 Hidden layer value + Threshold 2) (9) − × − Step5: The calculated results are anti-normalized through Equation (4).

Through the above steps, the porosity of a certain kind of particulate mixture can be accurately predicted.

4. Veriﬁcation and Application of Prediction Method For the purpose of evaluating model validity and accuracy, a static compression test was also completed in laboratory. The steel balls were used to compare with the virtual ball element model. Meanwhile, the relationship among the measured porosity, the simulated porosity and the predicted value was compared. In order to simulate the real composition of granular particles applied in highway Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 19

Output layer value = purelin(푊푒𝑖푔ℎ푡−2 × 퐻𝑖푑푑푒푛 푙푎푦푒푟 푣푎푙푢푒 + 푇ℎ푟푒푠ℎ표푙푑−2) (9) Step5: The calculated results are anti-normalized through Equation (4). Through the above steps, the porosity of a certain kind of particulate mixture can be accurately predicted.

4. Verification and Application of Prediction Method For the purpose of evaluating model validity and accuracy, a static compression test was also completed in laboratory. The steel balls were used to compare with the virtual ball element model. Appl.Meanwhile, Sci. 2020, 10the, 1693 relationship among the measured porosity, the simulated porosity and the predicted14 of 19 value was compared. In order to simulate the real composition of granular particles applied in engineering,highway engineer a greating number, a great ofnumber steel ballsof steel in balls diﬀerent in different sizes were sizes prepared were prepared and mixed and mixed in the in same the proportionsame proportion as uniformly as unifor asm possible,ly as possible, then sieved then tosieved several to several diﬀerent different size groups. size groups. The original The original particle sizeparticle distribution size distribution and sieved and results sieved of results the steel of the balls steel are balls shown are in shown Table 14in Tableand Figure 14 and9. Figure 9.

Table 14.14. Particle size distribution ofof thethe steelsteel balls.balls. Sieving Group (mm) Particle Size Distribution (mm) Sieving Group (mm) Particle Size Distribution (mm) 16.0–19.0 17, 18, 19 16.0–19.0 17, 18, 19 13.2–16.013.2–16.0 14, 15, 14, 15,16 16 9.5–13.29.5–13.2 10, 11, 10, 12, 11, 12,12.303 12.303 4.75–9.54.75–9.5 5, 6, 5, 7, 6, 8, 7, 9 8, 9 2.36–4.752.36–4.75 2.5, 2.5,3, 4 3, 4

Figure 9. Steel balls with didifferentﬀerent sizes.sizes.

AccordingAccording to to Table Table 14 1 and4 and Figure Figure9, every 9, every sieving sieving group group was mixed was mixed with several with di severalfferent different particle sizeparticle groups size uniformly. groups uniformly. For 9.5–13.2 For mm9.5–13 group,.2 mm 13.0 group, mm particles13.0 mm wereparticles not found,were not so found, 12.303 mmso 12.303 balls weremm balls added were to keepadded a continuousto keep a continuous and real size and distribution real size distribution in the steel in balls. the steel balls. Then, in order to make the results of laboratory and DEM comparable, the size of steel ball experiments’Then, in container order to make was exactly the results the same of laboratory as the DEM and model. DEM According comparable, to thediff erentsize of gradations, steel ball theexperiments’ steel balls container were mixed was in exactly a standard the same Marshall as the mold, DEM whose model. diameter According was to 100different mm as gradations, shown in Figurethe steel 10 .balls Because were there mixed was in no a fillerstandard or binder Marshall in this mold, mixture, whose universal diameter testing was machine100 mm wereas shown applied in toFigure compact 10. Btheecause mixed there steel was balls no with filler a static or binder pressure in thisof 600 mixture, kPa. Meanwhile, universal particles’ testing machine total volume were wasapplied measured to compact by the the displacement mixed steel method.balls with On a thestatic other pressure hand, of virtual 600 kPa. compression Meanwhile, tests particles’ on computer total and porosity prediction on BP neural network model were completed at the same time. The detailed test data is shown in the following Figure 11. Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 19 volume was measured by the displacement method. On the other hand, virtual compression tests on volume was measured by the displacement method. On the other hand, virtual compression tests on computer and porosity prediction on BP neural network model were completed at the same time. computer and porosity prediction on BP neural network model were completed at the same time. TheAppl. detailed Sci. 2020, 10test, 1693 data is shown in the following Figure 11. 15 of 19 The detailed test data is shown in the following Figure 11.

Figure 10. Steel balls in lab experiment. Figure 10. Steel balls in lab experiment.

0.4 0.4 0.39 0.39 0.38 0.38 0.37 0.37 0.36 Lab test

0.36 Lab test Porosity

Porosity 0.35 Virtual test 0.35 Virtual test 0.34 0.34 BP-Prediction BP-Prediction 0.33 0.33 0.32 0.32 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Ball test group Ball test group FigureFigure 11. 11. PorosityPorosity comparison comparison among among lab lab test, test, virtual virtual test test and and BP BPneural neural network network model model for steel for steelball Figure 11. Porosity comparison among lab test, virtual test and BP neural network model for steel ball testball. test. test. AsAs can can be be seen seen from from the the above above figure, figure, model prediction prediction accuracy accuracy for for the the steel steel ball ball test test was was very very As can be seen from the above figure, model prediction accuracy for the steel ball test was very highhigh and and model error was extremely slight. The The maximum maximum relative relative error error of of prediction prediction was was no no more more high and model error was extremely slight. The maximum relative error of prediction was no more thanthan 1.15%. This provedproved thethe credibility credibility of of the the prediction prediction model. model. Meanwhile, Meanwhile, the the results results of lab of testslab tests and than 1.15%. This proved the credibility of the prediction model. Meanwhile, the results of lab tests andvirtual virtual tests testswere werevery close, very whichclose, whichalso proved also proved that for thatthe sphere for the element-based sphere element model,-based su model,fficient and virtual tests were very close, which also proved that for the sphere element-based model, sufficientcredible raw credible data couldraw data be obtainedcould be byobtained DEM. by DEM. sufficient credible raw data could be obtained by DEM. 5. Reduction Factor Analysis Considering Particle Shape Effect on Mixture Porosity 5. Reduction Factor Analysis Considering Particle Shape Effect on Mixture Porosity 5. Reduction Factor Analysis Considering Particle Shape Effect on Mixture Porosity From the above illustration, a porosity prediction model for sphere element has been established. From the above illustration, a porosity prediction model for sphere element has been established. However,From asthe mentioned above illustration, in the Introduction, a porosity prediction paving materials model for in sphere reality element generally has have been complex established. but However, as mentioned in the Introduction, paving materials in reality generally have complex but similarHowever, particle as mentioned shape combinations, in the Introduction, which indicate paving thatmater shapeials in eff realityect is non-negligible generally have but complex consistent. but similar particle shape combinations, which indicate that shape effect is non-negligible but consistent. Therefore,similar particle a reduction shape combinations, factor to consider which particle indicate shape that e ffshapeect was effect introduced is non-negligible in this chapter. but consistent. Therefore, a reduction factor to consider particle shape effect was introduced in this chapter. Therefore,A gradation a reduction was selected factor to randomly consider forparticle comparing shape theeffect mixture was introduced porosity between in this spherechapter. elements A gradation was selected randomly for comparing the mixture porosity between sphere modelA and gradation real aggregate was selected shape model. randomly The volume for comparing of each particle the mixture size group porosity was: Volume between13.2 16.0 spheremm : elements model and real aggregate shape model. The volume of each particle size group− was: Volumeelements9.5 model13.2 mm : andVolume real4.75 aggregate9.5 mm : Volume shape 2.36 model.4.75 mm The= volume1 : 5 : 4 : of 1. each particle size group was: 푉표푙푢푚푒13.−2−16.0 푚푚: 푉표푙푢푚푒9.5−13.2 푚푚: 푉표푙푢푚푒4.75−−9.5 푚푚: 푉표푙푢푚푒2.36−4.75 푚푚 = 1: 5: 4: 1. 푉표푙푢푚푒A total13.2−16 number.0 푚푚: 푉표푙푢푚푒 of 15 DEM9.5−13.2 models 푚푚: 푉표푙푢푚푒 with4. di75−ff9erent.5 푚푚: real푉표푙푢푚푒 aggregated2.36−4.75 푚푚 shapes= 1: 5 were: 4: 1. built based on previous researches [33–37]. It should be noted that there is only one particle shape in each specimen to amplify its effect, as shown in Figure 12. Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 19

AA total total number number of of 15 15 DEM DEM models models with with different different real real aggregated aggregated shapes shapes were were built built based based on on previous researches [33–37]. It should be noted that there is only one particle shape in each specimen Appl.previous Sci. 2020 researches, 10, 1693 [33–37]. It should be noted that there is only one particle shape in each specimen16 of 19 toto amplify amplify its its effect effect, ,as as sho shownwn in in Figure Figure 12. 12.

FigureFigure 12. 12. TheThe The compacted compacted mixture mixture with with real real aggregate aggregate shape shape and and 15 15 aggregate aggregate shapes.shapes shapes. .

AllAll thethe the aggregateaggregate aggregate shapes shapes shapes used used used in thisin in this chapterthis chapter chapter were were were quite quite common.quite common. common. Although Although Although there arethere there some a arere special some some shapesspecialspecial in shapes shapes civil engineering, in in civil civil engineering, engineering, for instance, for for elongated instance, instance, particle, elongated elongated their particle, particle, volume their theirpercentages volume volume in percentages percentages mixture were in in generallymixturemixture were lowwere andgenerally generally strictly low controlled,low and and strictly strictly due tocontrolled controlled their poor, ,due engineeringdue to to their their poor properties.poor engineering engineering The model properties. properties. parameters The The weremodelmodel identical parameters parameters with spherewere were identical element-basedidentical with with sphere models.sphere element element In this- way,based-based these models. models. mixtures’ In In this this porosities way, way, these these were mixtures’ recordedmixtures’ andporositiesporosities plotted were were on therecorded recorded following and and Figureplotted plotted 13 on .on the the following following Figure Figure 13 13. .

0.50.5

0.4 0.4 PorosityPorosity of of sphere sphere elementselements model model Upper limit 0.30.3 Upper limit

LowLow limit limit

0.20.2

Mixture Porosity Mixture Mixture Porosity Mixture PorosityPorosity of of real real 0.10.1 aggregateaggregate shape shape modelmodel

00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 Particle shape number Particle shape number FigureFigure 13. 13.13. Mixture MixtureMixture porosity porosity porosity comparison comparison comparison between between between sphere sphere sphere elements elements elements model model model and and real andreal aggregate aggregate real aggregate shape shape shapemodelmodel model.. .

FromFrom Figure FigureFigure 13, 1313, the, the the red red red line line line represent represent representss sthe the mixture the mixture mixture porosity porosity porosity of of the the ofsphere sphere the sphereelements elements elements-based-based-based model, model, model,whichwhich was whichwas 0.381, 0.381, was while while 0.381, the the while green green the points points green refer pointsrefer to to refer15 15 mixture mixture to 15 mixture porosities porosities porosities in in 15 15 real real in 15aggregate aggregate real aggregate shapes shapes shapesrespectively.respectively. respectively. It It can can It be be can observed observed be observed that that thatthere there there i si s an anis anobvious obvious obvious difference difference diﬀerence between between between these these two two two models. models. models. Nevertheless,Nevertheless, this this didifference differenceﬀerence isi si s quitequite quite stablestable stable andand and consistentconsistent consistent among among 15 15 green green points.po points.ints. DetailedD Detailedetailed statistical statistical analysisanalysis has has been been done done as as shown shown in in the the following following TableTable Table 151 15.5. .

Appl. Sci. 2020, 10, 1693 17 of 19

Table 15. The conﬁdence limit calculation of mixture porosity of 15 real aggregate shape models.

Parameters Values The number of samples 15 The mean value of samples 0.218 The standard deviation of samples 0.023 Sampling average error 0.006 Probability level 0.95 Free degree 14 t-value 2.145 Error range 0.013 Conﬁdence lower limit 0.206 Conﬁdence upper limit 0.231

From Table 15, 95% conﬁdence interval has been determined and plotted as shown in Figure 13. Therefore, a shape reduction factor range was recommended considering the shape eﬀect through Equations (10) and (11).

Conﬁdence upper limit 0.231 Upper limit of shape reduction factor = = = 0.606 (10) Mixture porosity o f sphere model 0.381

Conﬁdence lower limit 0.206 Lower limit of shape reduction factor = = = 0.541 (11) Mixture porosity o f sphere model 0.381 When the prediction results based on sphere element models are multiplied by shape reduction factor, a more accurate result could be obtained.

6. Summary and Conclusions In this research, a porosity prediction model was established for granular mixtures through the DEM model and BPNN algorithm. A total of 400 mixes were simulated with the discrete element method to provide the database for BPNN training and testing. The prediction results were veriﬁed by steel ball experiments. Through this research, the following ﬁndings and conclusions were observed:

1. This study provided an efficient and detailed method to build a porosity prediction model according to DEM model and BPNN algorithm. After model training, testing in MATLAB and verifying in lab experiments, the model’s coefficients of determination could achieve 99%. 2. A suitable original database size was compared and recommended: prediction model accuracy could reach about 98% when the original data size was larger than 75. The amount of raw data can be determined according to different accuracy requirements. 3. A shape reduction factor was proposed to achieve the porosity reduction from sphere to real particle shape, which made the porosity prediction results closer to reality and easy to use. In this research, particle shapes were not considered as the primary control parameters, which will be considered in a future study. Evaluation is recommended of particle shapes through combining the findings of this research with experimental testing methods.

Author Contributions: Conceptualization, Y.L.; Data curation, M.L.; Funding acquisition, Y.L.; Methodology, M.L.; Resources, B.M.; Software, P.S.; Supervision, Z.Y.; Validation, P.S.; Writing—original draft, M.L.; Writing—review & editing, Y.L. and P.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Natural Science Foundation of China, grant number 51978074. The APC was funded by National Natural Science Foundation of China. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Appl. Sci. 2020, 10, 1693 18 of 19

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