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.     

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.     

The prediction of ultimate pure bending moment of concrete-filled steel tubes by adaptive neuro-fuzzy inference system (ANFIS)

In this study, different modelling techniques such as multiple regression and adaptive neuro-fuzzy inference system (ANFIS) are used for predicting the ultimate pure bending of concrete-filled steel tubes (CFTs). The behaviour of CFT under pure bending is complex and highly nonlinear; therefore, forward modelling techniques can have considerable limitations in practical situations where fast and reliable solutions are required. Linear multiple regression (LMR), nonlinear multiple regression (NLMR) and ANFIS models were trained and checked using a large database that was constructed and populated from the literature. The database comprises 72 pure bending tests conducted on fabricated and cold-formed tubes filled with concrete. Out of 72 tests, 48 tests were conducted by the second author. Input variables for the models are the same with those used by existing codes and practices such as the tube thickness, tube outside diameter, steel yield strength, strength of concrete and shear span. A practical application example, showing the translation of constructed ANFIS model into design equations suitable for hand calculations, was provided. A sensitivity analysis was conducted on ANFIS and multiple regression models. It was found that the ANFIS model is more sensitive to change in input variables than LMR and NLMR models. Predictions from ANFIS models were compared with those obtained from LMR, NLMR, existing theory and a number of available codes and standards. The results indicate that the ANFIS model is capable of predicting the ultimate pure bending of CFT with a high degree of accuracy and outperforms other common methods.

     

Predicting discharge capacity of triangular labyrinth side weir located on a straight channel by using an adaptive neuro-fuzzy technique

Side weirs are widely used for flow diversion in irrigation, land drainage, urban sewage systems and also in intake structures. It is essential to correctly predict the discharge coefficient for hydraulic engineers involved in the technical and economical design of side weirs. In this study, the discharge capacity of triangular labyrinth side weirs is estimated by using adaptive neuro-fuzzy inference system (ANFIS). Two thousand five hundred laboratory test results are used for determining discharge coefficient of triangular labyrinth side weirs. The performance of the ANFIS model is compared with multi nonlinear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the ANFIS technique could be employed successfully in modeling discharge coefficient from the available experimental data. There are good agreements between the measured values and the values obtained using the ANFIS model. It is found that the ANFIS model with RMSE of 0.0699 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.1019 and 0.1507, respectively.     

Rock strength assessment based on regression tree technique

Uniaxial compressive strength (UCS) is one of the most important parameters for investigation of rock behaviour in civil and mining engineering applications. The direct method to determine UCS is time consuming and expensive in the laboratory. Therefore, indirect estimation of UCS values using other rock index tests is of interest. In this study, extensive laboratory tests including density test, Schmidt hammer test, point load strength test and UCS test were conducted on 106 samples of sandstone which were taken from three sites in Malaysia. Based on the laboratory results, some new equations with acceptable reliability were developed to predict UCS using simple regression analysis. Additionally, results of simple regression analysis show that there is a need to propose UCS predictive models by multiple inputs. Therefore, considering the same laboratory results, multiple regression (MR) and regression tree (RT) models were also performed. To evaluate performance prediction of the developed models, several performance indices, i.e. coefficient of determination (R ²), variance account for and root mean squared error were examined. The results indicated that the RT model can predict UCS with higher performance capacity compared to MR technique. R ² values of 0.857 and 0.801 for training and testing datasets, respectively, suggests the superiority of the RT model in predicting UCS, while these values are obtained as 0.754 and 0.770 for MR model, respectively.     

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.

     

Flood flow forecasting using ANN,ANFIS and regression models

Flood prediction is an important for the design, planning and management of water resources systems. This study presents the use of artificial neural networks (ANN), adaptive neuro-fuzzy inference systems (ANFIS), multiple linear regression (MLR) and multiple nonlinear regression (MNLR) for forecasting maximum daily flow at the outlet of the Khosrow Shirin watershed, located in the Fars Province of Iran. Precipitation data from four meteorological stations were used to develop a multilayer perceptron topology model. Input vectors for simulations included the original precipitation data, an area-weighted average precipitation and antecedent flows with one- and two-day time lags. Performances of the models were evaluated with the RMSE and the R ². The results showed that the area-weighted precipitation as an input to ANNs and MNLR and the spatially distributed precipitation input to ANFIS and MLR lead to more accurate predictions (e.g., in ANNs up to 2.0 m³ s^?1 reduction in RMSE). Overall, the MNLR was shown to be superior (R ² = 0.81 and RMSE = 0.145 m³ s^?1) to ANNs, ANFIS and MLR for prediction of maximum daily flow. Furthermore, models including antecedent flow with one- and two-day time lags significantly improve flow prediction. We conclude that nonlinear regression can be applied as a simple method for predicting the maximum daily flow.     

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.     

Multiple regression,ANN and ANFIS models for prediction of backbreak in the open pit blasting

Backbreak is one of the undesirable effects of blasting operations causing instability in mine walls, falling down the machinery, improper fragmentation and reduction in efficiency of drilling. Backbreak can be affected by various parameters such as the rock mass properties, blasting geometry and explosive properties. In this study, the application of the artificial neural network (ANN), an adaptive neuro-fuzzy inference system (ANFIS) for prediction of backbreak, was described and compared with the traditional statistical model of multiple regression. The performance of these models was assessed through the root mean square error, correlation coefficient (R ²) and mean absolute percentage error. As a result, it was found that the constructed ANFIS exhibited a higher performance than the ANN and multiple regression for backbreak prediction.     

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.

     

Adaptive neuro-fuzzy inference system–based model for elevation–surface area–storage interrelationships

In the developing of an optimal operation schedule for dams and reservoirs, reservoir simulation is one of the critical steps that must be taken into consideration. For reservoirs to have more reliable and flexible optimization models, their simulations must be very accurate. However, a major problem with this simulation is the phenomenon of nonlinearity relationships that exist between some parameters of the reservoir. Some of the conventional methods use a linear approach in solving such problems thereby obtaining not very accurate simulation most especially at extreme values, and this greatly influences the efficiency of the model. One method that has been identified as a possible replacement for ANN and other common regression models currently in use for most analysis involving nonlinear cases in hydrology and water resources–related problems is the adaptive neuro-fuzzy inference system (ANFIS). The use of this method and two other different approaches of the ANN method, namely feedforward back-propagation neural network and radial basis function neural network, were adopted in the current study for the simulation of the relationships that exist between elevation, surface area and storage capacity at Langat reservoir system, Malaysia. Also, another model, auto regression (AR), was developed to compare the analysis of the proposed ANFIS and ANN models. The major revelation from this study is that the use of the proposed ANFIS model would ensure a more accurate simulation than the ANN and the classical AR models. The results obtained showed that the simulations obtained through ANFIS were actually more accurate than those of ANN and AR; it is thus concluded that the use of ANFIS method for simulation of reservoir behavior will give better predictions than the use of any new or existing regression models.     

Rough set and PSO-based ANFIS approaches to modeling customer satisfaction for affective product design

Facing fierce competition in marketplaces, companies try to determine the optimal settings of design attribute of new products from which the best customer satisfaction can be obtained. To determine the settings, customer satisfaction models relating affective responses of customers to design attributes have to be first developed. Adaptive neuro-fuzzy inference systems (ANFIS) was attempted in previous research and shown to be an effective approach to address the fuzziness of survey data and nonlinearity in modeling customer satisfaction for affective design. However, ANFIS is incapable of modeling the relationships that involve a number of inputs which may cause the failure of the training process of ANFIS and lead to the ‘out of memory’ error. To overcome the limitation, in this paper, rough set (RS) and particle swarm optimization (PSO) based-ANFIS approaches are proposed to model customer satisfaction for affective design and further improve the modeling accuracy. In the approaches, the RS theory is adopted to extract significant design attributes as the inputs of ANFIS and PSO is employed to determine the parameter settings of an ANFIS from which explicit customer satisfaction models with better modeling accuracy can be generated. A case study of affective design of mobile phones is used to illustrate the proposed approaches. The modeling results based on the proposed approaches are compared with those based on ANFIS, fuzzy least-squares regression (FLSR), fuzzy regression (FR), and genetic programming-based fuzzy regression (GP-FR). Results of the training and validation tests show that the proposed approaches perform better than the others in terms of training and validation errors.     

Application of adaptive neuro-fuzzy technique and regression models to predict the compressive strength of geopolymer composites

This article introduces an adaptive network-based fuzzy inference system (ANFIS) model and two linear and nonlinear regression models to predict the compressive strength of geopolymer composites. Geopolymers are highly complex materials which involve many variables which make modeling its properties very difficult. There is no systematic approach in the mix design for geopolymers. The amounts of silica modulus, Na₂O content, w/b ratios, and curing time have a great influence on the compressive strength. In this study, by developing and comparing parametric linear and nonlinear regressions and ANFIS models, we dealt with predicting the compressive strength of geopolymer composites for possible use in mix-design framework considering the mentioned complexities. ANFIS model developed by generalized bell-shaped membership function was recognized the best approach, and the prediction results of linear and nonlinear regression models as empirical methods showed the weakness of these models comparing ANFIS model.

     

Modelling of evaporation from the reservoir of Yuvacik dam using adaptive neuro-fuzzy inference systems

Adaptive neuro-fuzzy inference system (ANFIS) models are proposed as an alternative approach of evaporation estimation for Yuvacik Dam. This study has three objectives: (1) to develop ANFIS models to estimate daily pan evaporation from measured meteorological data; (2) to compare the ANFIS model to the multiple linear regression (MLR) model; and (3) to evaluate the potential of ANFIS model. Various combinations of daily meteorological data, namely air temperature, relative humidity, solar radiation and wind speed, are used as inputs to the ANFIS so as to evaluate the degree of effect of each of these variables on daily pan evaporation. The results of the ANFIS model are compared with MLR model. Mean square error, average absolute relative error and coefficient of determination statistics are used as comparison criteria for the evaluation of the model performances. The ANFIS technique whose inputs are solar radiation, air temperature, relative humidity and wind speed, gives mean square errors of 0.181 mm, average absolute relative errors of 9.590% mm, and determination coefficient of 0.958 for Yuvacik Dam station, respectively. Based on the comparisons, it was found that the ANFIS technique could be employed successfully in modelling evaporation process from the available climatic data.     

Predicting the occurrence of adverse events using an adaptive neuro-fuzzy inference system (ANFIS) approach with the help of ANFIS input selection

This study presents an adaptive neuro-fuzzy inference system (ANFIS) approach performed to estimate the number of adverse events where the dependent variables are adverse events leading to four types of variables: number of people killed, wounded, hijacked and total number of adverse events. Fourteen infrastructure development projects were selected based on allocated budgets values at different time periods, population density, and previous month adverse event numbers selected as independent variables. Firstly, number of independent variables was reduced by using ANFIS input selection approach. Then, several ANFIS models were performed and investigated for Afghanistan and the whole country divided into seven regions for analysis purposes. Performances of models were assessed and compared based on the mean absolute errors. The difference between observed and estimated value was also calculated within \({\pm }1\) range with values around 90 %. We included multiple linear regression (MLR) model results to assess the predictive power of the ANFIS approach, in comparison to a traditional statistical approach. When the model accuracy was calculated according to the performance metrics, ANFIS showed greater predictive accuracy than MLR analysis, as indicated by experimental results. As a result of this study, we conclude that ANFIS is able to estimate the occurrence of adverse events according to economical infrastructure development project data.     

Synthesis of the Resultant Force Position on a Radial Ply Tire of Off-Road Vehicle with a Comparative Trend Between Some Soft Computing Techniques

To obtain a qualitative understanding of tractive performance parameters, ride comfort, vibration control and the design of an off-road vehicle suspension system, it is essential to find the resultant force position on the wheel. To this aim, a soil bin facility assisted with a single-wheel tester was used for the synthesis of the objective parameter. Four levels of slip were induced to the wheel along with three levels of velocity and two wheel loads. The stochastic characteristic of soil–wheel interactions promoted the authors to apply two promising artificial intelligence approaches of artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) and compare the results with the statistical approach of multiple linear regression (MLR). Various structures of ANN and ANFIS tools were constructed to obtain the best representations. Two statistical performance criteria of mean squared error (MSE) and coefficient of determination \((R^{2})\) were employed to assess the potential of the constructed models. In view of the employed criteria, it was divulged that the supervised ANN outperformed the ANFIS model with MSE and \(R^{2}\) values of 0.02615 and 0.93628, respectfully, where ANFIS model yielded MSE and \(R^{2}\) values equal to 0.0439 and 0.8494, respectfully.     

An expert system for predicting aeration performance of weirs by using ANFIS

A free overfall jet from a weir plunging into downstream water causes entrainment of the air bubbles if the free overfall jet velocity exceeds a certain critical value and hence aeration occurs. This study investigates the free overfall jets from triangular sharp-crested weirs and effect on their air entrainment rate and the aeration efficiency. An expert system based on adaptive network based fuzzy inference system (ANFIS) was obtained for predicting air entrainment rate and aeration efficiency of weirs. The performance of ANFIS model was compared with multi nonlinear and linear regression models. There were good agreements between the measured values and the values obtained using the ANFIS model.     

优化岭参数的非线性岭回归及4-CBA含量软测量

针对二甲苯氧化反应过程中影响主要副产物对羧基苯甲醛含量的因素众多且呈高度非线性的问题,提出基于优化岭参数的非线性岭回归MNRR算法,并应用于建立4 CBA含量软测量模型,获得满意的结果.MNRR采用非线性变换对原始模式特征空间进行扩张,以预测性能为指标,采用进化算法确定最佳岭参数,最终建立具有强非线性表达能力以及预测性能良好的模型.与非线性最小二乘回归和基于广义交叉有效性逐步估计岭参数的非线性岭回归相比,MNRR模型具有更高的预测精度且克服了传统岭回归算法最佳岭参数难以确定的缺点.     

Application of ANFIS Model for Thailand’s Electric Vehicle Consumption

Generally, road transport is a major energy-consuming sector. Fuel consumption of each vehicle is an important factor that affects the overall energy consumption, driving behavior and vehicle characteristic are the main factors affecting the change of vehicle fuel consumption. It is difficult to analyze the influence of fuel consumption with multiple and complex factors. The Adaptive Neuro-Fuzzy Inference System (ANFIS) approach was employed to develop a vehicle fuel consumption model based on multivariate input. The ANFIS network was constructed by various experiments based on the ANFIS Parameter setting. The performance of the ANFIS network was validated using Root Mean Square Error (RMSE) and Mean Average Error (MAE) which related to the setting of ANFIS parameters. The experimental results indicated that the training data sample, number, and type of membership functions are the most important factor affecting the performance of the ANFIS network. However, the number of epochs does not necessarily significantly improve the system performance, too many the number of epochs setting may not provide the best results and lead to excessive responding time. The results also demonstrate that three factors, consisted of the engine size, driving speed, and the number of passengers, are important factors that influence the change of vehicle fuel consumption. The selected ANFIS models with minimum error can be properly and efficiently used to predict vehicle fuel consumption for Thailand’s road transport sector.     

Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels

Side weirs have been extensively used in hydraulic and environmental engineering applications. The discharge coefficient of the triangular labyrinth side weirs is 1.5-4.5 times higher than that of rectangular side weirs. This study aims to estimate the discharge coefficient (C_d) of triangular labyrinth side weir in curved channel by using artificial neural networks (ANN). In this study, 7963 laboratory test results are used for determining the C_d. The performance of the ANN model is compared with multiple nonlinear and linear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modeling discharge coefficient from the available experimental data. There were good agreements between the measured values and the values obtained using the ANN model. It was found that the ANN model with RMSE of 0.1658 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.2054 and 0.2926, respectively.