Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances

Uniaxial compressive strength (UCS) of rock is crucial for any type of projects constructed in/on rock mass. The test that is conducted to measure the UCS of rock is expensive, time consuming and having sample restriction. For this reason, the UCS of rock may be estimated using simple rock tests such as point load index (I _s(50)), Schmidt hammer (R _n) and p-wave velocity (V _p) tests. To estimate the UCS of granitic rock as a function of relevant rock properties like R _n, p-wave and I _s(50), the rock cores were collected from the face of the Pahang–Selangor fresh water tunnel in Malaysia. Afterwards, 124 samples are prepared and tested in accordance with relevant standards and the dataset is obtained. Further an established dataset is used for estimating the UCS of rock via three-nonlinear prediction tools, namely non-linear multiple regression (NLMR), artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). After conducting the mentioned models, considering several performance indices including coefficient of determination (R ²), variance account for and root mean squared error and also using simple ranking procedure, the models were examined and the best prediction model was selected. It is concluded that the R ² equal to 0.951 for testing dataset suggests the superiority of the ANFIS model, while these values are 0.651 and 0.886 for NLMR and ANN techniques, respectively. The results pointed out that the ANFIS model can be used for predicting UCS of rocks with higher capacity in comparison with others. However, the developed model may be useful at a preliminary stage of design; it should be used with caution and only for the specified rock types.     

Uniaxial compressive strength prediction through a new technique based on gene expression programming

Proper estimation of rock strength is a critical task for evaluation and design of some geotechnical applications such as tunneling and excavation. Uniaxial compressive strength (UCS) test can be measured directly in the laboratory; nevertheless, the direct UCS determination is time-consuming and expensive. In this study, feasibility of gene expression programming (GEP) model in indirect determination of UCS values of sandstone rock samples is examined. In this regard, several laboratory tests including Brazilian test, density test, slake durability test and UCS test were conducted on 47 samples of sandstone which were collected from the Dengkil, Malaysia. Considering multiple inputs, several GEP models were constructed to estimate UCS of the rock and finally, the best GEP model was selected. In order to indicate capability of the proposed GEP model, linear multiple regression (LMR) was also performed. It was found that the GEP model is superior to LMR one in terms of applied performance indices. Based on coefficient of determination (R ²) of testing datasets, by proposing GEP model, it can be improved from 0.930 (which was obtained by LMR model) to 0.965. As a result, it is concluded that the proposed models in this study, could be utilized to estimate UCS of similar rock type in practice.

     

Prediction of unconfined compressive strength of rock surrounding a roadway using artificial neural network

The unconfined compressive strength (UCS) of rocks is an important design parameter in rock engineering and geotechnics, which is required and determined for rock mechanical studies in mining and civil projects. This parameter is usually determined through a laboratory UCS test. Since the preparation of high-quality samples is difficult, expensive and time consuming for laboratory tests, development of predictive models for determining the mechanical properties of rocks seems to be essential in rock engineering. In this study, an attempt was made to develop an artificial neural network (ANN) and multivariable regression analysis (MVRA) models in order to predict UCS of rock surrounding a roadway. For this, a database of laboratory tests was prepared, which includes rock type, Schmidt hardness, density and porosity as input parameters and UCS as output parameter. To make a database (including 93 datasets), different rock samples, ranging from weak to very strong types, are used. To compare the performance of developed models, determination coefficient (R ²), variance account for (VAF), mean absolute error (E _a) and mean relative error (E _r) indices between predicted and measured values were calculated. Based on this comparison, it was concluded that performance of the ANN model is considerably better than the MVRA model. Further, a sensitivity analysis shows that rock density and Schmidt hardness were recognized as the most effective parameters, whereas porosity was considered as the least effective input parameter on the ANN model output (UCS) in this study.     

An intelligent approach to predict unconfined compressive strength of rock surrounding access tunnels in longwall coal mining

Unconfined compressive strength (UCS) of rocks is one of the most important parameters in rock engineering, engineering geology, and mining projects. In the laboratory determination of UCS, high-quality samples are necessary; in which preparing of core samples has several limits, as it is difficult, expensive, and time-consuming. For this, development of predictive models to determine the UCS of rocks seems to be an attractive research. In this study, an intelligent approach based on the Mamdani fuzzy model was utilized to predict UCS of rock surrounding access tunnels in longwall coal mining. To approve the capability of this approach, the obtained results are compared to the results of statistical model. A database containing 93 rock sample records, ranging from weak to very strong rock types, was used to develop and test the models. For the evaluation of models performance, determination coefficient (R ²), root mean square error, and variance account for indices were used. Based on this comparison, it was concluded that performance of fuzzy model is considerably better than statistical model. Also, the fuzzy model results indicate very close agreement for the UCS with the laboratory measurements. Furthermore, the fuzzy model sensitivity analysis shows that Schmidt hardness and porosity are the most and least effective parameters on the UCS, respectively.     

Application of improved support vector regression model for prediction of deformation modulus of a rock mass

Deformation modulus of a rock mass is one of the crucial parameters used in the design of surface and underground rock engineering structures. Determination of this parameter by testing cylindrical core samples is almost impossible due to the presence of discontinuities. Due to the problems in determining the deformability of jointed rock masses at the laboratory-scale, various in situ test methods such as plate loading tests, dilatometer etc. have been developed. Although these methods are currently the best techniques, they are expensive and time-consuming, and present operational problems. To overcome this difficulty, in this paper, presents the results of the application of hybrid support vector regression (SVR) with harmony search algorithm , differential evolution algorithm and particle swarm optimization algorithm (PSO). The optimized models were applied to available data given in open source literature and the performance of optimization algorithm was assessed by virtue of statistical criteria. In these models, rock mass rating (RMR), depth, uniaxial compressive strength of intact rock (UCS) and elastic modulus of intact rock (E _i) were utilized as the input parameters, while the deformation modulus of a rock mass was the output parameter. The comparative results revealed that hybrid of PSO and SVR yield robust model which outperform other models in term of higher squared correlation coefficient (R ²) and variance account for (VAF) and lower mean square error (MSE), root mean squared error (RMSE) and mean absolute percentage error (MAPE).     

An application of adaptive neuro fuzzy inference system for estimating the uniaxial compressive strength of certain granitic rocks from their mineral contents

The uniaxial compressive strength (UCS) of rocks is an important intact rock parameter, and it is commonly used for various engineering applications. This parameter is mainly controlled by the mineralogical and textural characteristics of rocks. In this study, a soft computing method, an adaptive neuro-fuzzy inference system (ANFIS), was employed to estimate UCS from the mineral contents of certain granitic rocks selected from Turkey; nonlinear multiple regression analysis was then employed to validate these estimations. Five nonlinear multiple regressions and ANFIS models were constructed with three inputs: quartz, orthoclase and plagioclase. To determine the optimal model, various performance indices (R, values account for and root mean square error) were determined, and the model obtained from dataset #3 was selected as the optimal model. The coefficients of correlation for the nonlinear multiple regression and ANFIS models were 0.87 and 0.91, respectively. Thus, both models yielded acceptable results, and the ANFIS is a suitable method for estimating the UCS of rocks.     

Evaluation and prediction of flyrock resulting from blasting operations using empirical and computational methods

Mines, quarries and construction sites face environmental impacts, such as flyrock, due to blasting operations. Flyrock may cause damage to structures and injury to human. Therefore, flyrock prediction is required to determine safe blasting zone. In this regard, 232 blasting operations were investigated in five granite quarries, Malaysia. Blasting parameters comprising maximum charge per delay and powder factor were prepared to predict flyrock using empirical and intelligent methods. An empirical graph was proposed to predict flyrock distance for different powder factor values. In addition, using the same datasets, two intelligent systems, namely artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were used to predict flyrock. Considering some model performance indices including coefficient of determination (R ²), value account for and root mean squared error and also using simple ranking procedure, the best flyrock prediction models were selected. It was found that the ANFIS model can predict flyrock with higher performance capacity compared to ANN predictive model. R ² values of testing datasets are 0.925 and 0.964 for ANN and ANFIS techniques, respectively, suggesting the superiority of the ANFIS technique in predicting flyrock.     

Rock strength estimation: a PSO-based BP approach

Application of back-propagation (BP) artificial neural network (ANN) as an accurate, practical and quick tool in indirect estimation of uniaxial compressive strength (UCS) of rocks has recently been highlighted in the literature. This is mainly due to difficulty in direct determination of UCS in laboratory as preparing the core samples for this test is troublesome and time-consuming. However, ANN technique has some limitations such as getting trapped in local minima. These limitations can be minimized by combining the ANNs with robust optimization algorithms like particle swarm optimization (PSO). This paper gives insight into development of a hybrid PSO–BP predictive model of UCS. For this reason, dataset comprising the results of 228 laboratory tests including dry density, moisture content, P wave velocity, point load index test, slake durability index and UCS was prepared. These tests were conducted on 38 sandstone samples which were taken from two excavation sites in Malaysia. Findings showed that PSO–BP model performs well in predicting UCS. Nevertheless, to compare the prediction performance of the PSO–BP model, the UCS is predicted using ANN-based PSO and BP models. The correlation coefficient, R, values equal to 0.988 and 0.999 for training and testing datasets, respectively, suggest that the PSO–BP model outperforms the other predictive models.

     

Feasibility of PSO–ANFIS model to estimate rock fragmentation produced by mine blasting

Desired rock fragmentation is the main goal of the blasting operation in surface mines, civil and tunneling works. Therefore, precise prediction of rock fragmentation is very important to achieve an economically successful outcome. The primary objective of this article is to propose a new model for forecasting the rock fragmentation using adaptive neuro-fuzzy inference system (ANFIS) in combination with particle swarm optimization (PSO). The proposed PSO–ANFIS model has been compared with support vector machines (SVM), ANFIS and nonlinear multiple regression (MR) models. To construct the predictive models, 72 blasting events were investigated, and the values of rock fragmentation as well as five effective parameters on rock fragmentation, i.e., specific charge, stemming, spacing, burden and maximum charge used per delay were measured. Based on several statistical functions [e.g., coefficient of correlation (R ²) and root-mean-square error (RMSE)], it was found that the PSO–ANFIS (with R ² = 0.89 and RMSE = 1.31) performs better than the SVM (with R ² = 0.83 and RMSE = 1.66), ANFIS (with R ² = 0.81 and RMSE = 1.78) and nonlinear MR (with R ² = 0.57 and RMSE = 3.93) models. Finally, the sensitivity analysis shows that the burden and maximum charge used per delay have the least and the most effects on the rock fragmentation, respectively.

     

Prediction of seismic slope stability through combination of particle swarm optimization and neural network

One of the main concerns in geotechnical engineering is slope stability prediction during the earthquake. In this study, two intelligent systems namely artificial neural network (ANN) and particle swarm optimization (PSO)–ANN models were developed to predict factor of safety (FOS) of homogeneous slopes. Geostudio program based on limit equilibrium method was utilized to obtain 699 FOS values with different conditions. The most influential factors on FOS such as slope height, gradient, cohesion, friction angle and peak ground acceleration were considered as model inputs in the present study. A series of sensitivity analyses were performed in modeling procedures of both intelligent systems. All 699 datasets were randomly selected to 5 different datasets based on training and testing. Considering some model performance indices, i.e., root mean square error, coefficient of determination (R ²) and value account for (VAF) and using simple ranking method, the best ANN and PSO–ANN models were selected. It was found that the PSO–ANN technique can predict FOS with higher performance capacities compared to ANN. R ² values of testing datasets equal to 0.915 and 0.986 for ANN and PSO–ANN techniques, respectively, suggest the superiority of the PSO–ANN technique.     

Design and implementation of a new tuned hybrid intelligent model to predict the uniaxial compressive strength of the rock using SFS-ANFIS

This study proposes a novel design to systematically optimize the parameters for the adaptive neuro-fuzzy inference system (ANFIS) model using stochastic fractal search (SFS) algorithm. To affirm the efficiency of the proposed SFS-ANFIS model, the predicting results were compared with ANFIS and three hybrid methodologies based on ANFIS combined with genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO). Accurate prediction of uniaxial compressive strength (UCS) is of great significance for all geotechnical projects such as tunnels and dams. Hence, this study proposes the use of SFS-ANFIS, GA-ANFIS, DE-ANFIS, PSO-ANFIS, and ANFIS models to predict UCS. In this regard, the fresh water tunnel of Pahang–Selangor located in Malaysia was considered and the requirement data samples were collected. Different statistical metrics such as coefficient of determination (R²) and mean absolute error were used to evaluate the models. Referring to the efficiency results of SFS-ANFIS, it can be found that the SFS-ANFIS (with the R² of 0.981) has higher ability than PSO-ANFIS, DE-ANFIS, GA-ANFIS, and ANFIS models in predicting the UCS.

     

A new combination of artificial neural network and <Emphasis Type="Italic">K</Emphasis>-nearest neighbors models to predict blast-induced ground vibration and air-overpressure

Blasting operation is widely used method for rock excavation in mining and civil works. Ground vibration and air-overpressure (AOp) are two of the most detrimental effects induced by blasting. So, evaluation and prediction of ground vibration and AOp are essential. This paper presents a new combination of artificial neural network (ANN) and K-nearest neighbors (KNN) models to predict blast-induced ground vibration and AOp. Here, this combination is abbreviated using ANN-KNN. To indicate performance of the ANN-KNN model in predicting ground vibration and AOp, a pre-developed ANN as well as two empirical equations, presented by United States Bureau of Mines (USBM), were developed. To construct the mentioned models, maximum charge per delay (MC) and distance between blast face and monitoring station (D) were set as input parameters, whereas AOp and peak particle velocity (PPV), as a vibration index, were considered as output parameters. A database consisting of 75 datasets, obtained from the Shur river dam, Iran, was utilized to develop the mentioned models. In terms of using three performance indices, namely coefficient correlation (R ²), root mean square error and variance account for, the superiority of the ANN-KNN model was proved in comparison with the ANN and USBM equations.     

Several non-linear models in estimating air-overpressure resulting from mine blasting

This research presents several non-linear models including empirical, artificial neural network (ANN), fuzzy system and adaptive neuro-fuzzy inference system (ANFIS) to estimate air-overpressure (AOp) resulting from mine blasting. For this purpose, Miduk copper mine, Iran was investigated and results of 77 blasting works were recorded to be utilized for AOp prediction. In the modeling procedure of this study, results of distance from the blast-face and maximum charge per delay were considered as predictors. After constructing the non-linear models, several performance prediction indices, i.e. root mean squared error (RMSE), variance account for (VAF), and coefficient of determination (R ²) and total ranking method are examined to choose the best predictive models and evaluation of the obtained results. It is obtained that the ANFIS model is superior to other utilized techniques in terms of R ², RMSE, VAF and ranking herein. As an example, RMSE values of 5.628, 3.937, 3.619 and 2.329 were obtained for testing datasets of empirical, ANN, fuzzy and ANFIS models, respectively, which indicate higher performance capacity of the ANFIS technique to estimate AOp compared to other implemented methods.     

A new hybrid ANFIS–PSO model for prediction of peak particle velocity due to bench blasting

In this paper, a novel hybrid approach is proposed for predicting peak particle velocity (PPV) due to bench blasting in open pit mines. The proposed approach is based on the combination of adaptive neuro-fuzzy inference system (ANFIS) and particle swarm optimization (PSO). In this approach, the PSO is used to improve the performance of ANFIS. Furthermore, a model is developed based on support vector regression (SVR) approach. The models are trained and tested based on actual data compiled from 120 blast rounds in Sarcheshmeh copper mine. To determine the accuracy and efficiency of ANFIS–PSO and SVR models, a statistical model (USBM equation) is applied. According to the obtained results, both techniques can be used to predict the PPV, but the comparison of models shows that the ANFIS–PSO model provides better results. Root mean square error (RMSE), variance account for (VAF), and coefficient of determination (R ²) indices were obtained as 1.83, 93.37 and 0.957 for ANFIS–PSO model, respectively.     

Estimating the energy production of the wind turbine using artificial neural network

Due to fluctuating weather conditions, estimating wind energy potential is still a significant problem. Artificial neural networks (ANNs) have been commonly used in short-term and just-in-time modeling of wind power generation systems based on main weather parameters such as wind speed, temperature, and humidity. Two different datasets called hourly main weather data (MWD) and daily sub-data (DSD) are used to estimate a wind turbine power generation in this study. MWD are based on historically observed wind speed, wind direction, air temperature, and pressure parameters. Besides, DSD created with statistical terms of MWD consist of maximum, minimum, mean, standard deviation, skewness, and kurtosis values. The main purpose of this study in particular was to develop a multilinear model representing the relationship between the DSD with the calculated minimum (P _min) and maximum (P _max) power generation values as well as the total power generation (P _sum) produced in a day by a wind turbine based on the MWD. While simulation values of the turbine, P _min, P _max, and P _sum, were used as the separately dependent parameters, DSD were determined as independent parameters in the estimation models. Stepwise regression was used to determine efficient independent parameters on the dependent parameters and to remove the inefficient parameters in the exploratory phase of study. These efficient parameters and simulated power generation values were used for training and testing the developed ANN models. Accuracy test results show that interoperability framework models based on stepwise regression and the neural network models are more accurate and more reliable than a linear approach.     

A regression model based on the nearest centroid neighborhood

The renowned k-nearest neighbor decision rule is widely used for classification tasks, where the label of any new sample is estimated based on a similarity criterion defined by an appropriate distance function. It has also been used successfully for regression problems where the purpose is to predict a continuous numeric label. However, some alternative neighborhood definitions, such as the surrounding neighborhood, have considered that the neighbors should fulfill not only the proximity property, but also a spatial location criterion. In this paper, we explore the use of the k-nearest centroid neighbor rule, which is based on the concept of surrounding neighborhood, for regression problems. Two support vector regression models were executed as reference. Experimentation over a wide collection of real-world data sets and using fifteen odd different values of k demonstrates that the regression algorithm based on the surrounding neighborhood significantly outperforms the traditional k-nearest neighborhood method and also a support vector regression model with a RBF kernel.     

Rock brittleness prediction through two optimization algorithms namely particle swarm optimization and imperialism competitive algorithm

Brittleness index (BI) is a significant rock parameter when dealing with projects performed in rocks. The main goal of this research work is to propose the novel practical models to predict the BI through particle swarm optimization (PSO) and imperialism competitive algorithm (ICA). For this aim, two forms of equations, i.e., linear and power are considered and the weights of these equations are optimized by PSO and ICA. In the other words, four predictive models, namely ICA linear, ICA power, PSO linear, and PSO power models are developed to predict BI in this study. In the modeling of the predictive models, 79 datasets are used, so that Schmidt hammer rebound number, wave velocity, density, and Point Load Index (Is₅₀) are selected as the independent (input) parameters and the BI values are considered as the dependent (output) parameter. Then, the performances of the proposed predicting models are checked using two error indices, namely coefficient correlation (R²) and root mean squared error (RMSE). The results showed that the PSO power model has superior fitting specification for the prediction of the BI compared to the other prediction models and is quite practical for use. As a result, linear and power models of PSO received higher performance prediction compared to ICA. PSO power (with R² train = 0.937, R² test = 0.959, RMSE train = 0.377 and RMES test = 0.289) showed the most powerful technique to predict BI of the granite samples.

     

Estimating the Penetration Rate in Diamond Drilling in Laboratory Works Using the Regression and Artificial Neural Network Analysis

Diamond drilling has been widely used in the different civil engineering projects. The prediction of penetration rate in the drilling is especially useful for the feasibility studies. In this study, the predictability of penetration rate for the diamond drilling was investigated from the operational variables and the rock properties such as the uniaxial compressive strength, the tensile strength and the relative abrasiveness. Both the multiple regression and the artificial neural networks (ANN) analysis were used in the study. Very good models were derived from ANN analysis for the prediction of penetration rate. The comparison of ANN models with the regression models indicated that ANN models were much more reliable than the regression models. It is concluded that the penetration rate for the diamond drilling can be reliably estimated from the uniaxial compressive strength, the tensile strength and the relative abrasiveness using the ANN models.     

Genetic programing and non-linear multiple regression techniques to predict backbreak in blasting operation

In addition to all benefits of blasting in mining and civil engineering applications, it has some undesirable environmental impacts. Backbreak is an unwanted phenomenon of blasting which can cause instability of mine walls, decreasing efficiency of drilling, falling down of machinery, etc. Recently, the use of new approaches such as artificial intelligence (AI) is greatly recommended by many researchers. In this paper, a new AI technique namely genetic programing (GP) was developed to predict BB. To prepare a sufficient database, 175 blasting works were investigated in Sungun copper mine, Iran. In these operations, the most influential parameters on BB including burden, spacing, stemming length, powder factor and stiffness ratio were measured and used to develop BB predictive models. To demonstrate capability of GP technique, a non-linear multiple regression (NLMR) model was also employed for prediction of BB. Value account for (VAF), root mean square error (RMSE) and coefficient of determination (R ²) were used to control the capacity performance of the predictive models. The performance indices obtained by GP approach indicate the higher reliability of GP compared to NLMR model. RMSE and VAF values of 0.327 and 97.655, respectively, for testing datasets of GP approach reveal the superiority of this model in predicting BB, while these values were obtained as 0.865 and 81.816, respectively, for NLMR model.     

GA-SVR: a novel hybrid data-driven model to simulate vertical load capacity of driven piles

Piles are widely applied to substructures of various infrastructural buildings. Soil has a complex nature; thus, a variety of empirical models have been proposed for the prediction of the bearing capacity of piles. The aim of this study is to propose a novel artificial intelligent approach to predict vertical load capacity of driven piles in cohesionless soils using support vector regression (SVR) optimized by genetic algorithm (GA). To the best of our knowledge, no research has been developed the GA-SVR model to predict vertical load capacity of driven piles in different timescales as of yet, and the novelty of this study is to develop a new hybrid intelligent approach in this field. To investigate the efficacy of GA-SVR model, two other models, i.e., SVR and linear regression models, are also used for a comparative study. According to the obtained results, GA-SVR model clearly outperformed the SVR and linear regression models by achieving less root mean square error (RMSE) and higher coefficient of determination (R²). In other words, GA-SVR with RMSE of 0.017 and R² of 0.980 has higher performance than SVR with RMSE of 0.035 and R² of 0.912, and linear regression model with RMSE of 0.079 and R² of 0.625.