Modification of rock mass rating system using soft computing techniques

Classification systems such as rock mass rating (RMR) are used to evaluate rock mass quality. This paper intended to evaluate RMR based on a fuzzy clustering algorithm to improve linguistic and empirical criteria for the RMR classification system. In the proposed algorithm, membership functions were first extracted for each RMR parameter based on the questionnaires filled out by experts. RMR clustering algorithm was determined by considering the percent importance of each parameter in the RMR classification system. In all implementation stages of the proposed algorithm, no empirical judgment was made in determining the classification classes in the RMR system. According to the obtained results, the proposed algorithm is a powerful tool to modify the rock mass rating system and can be generalized for future research.

     

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).     

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.     

Modelling sovereign credit ratings: Neural networks versus ordered probit

Sovereign credit ratings are becoming increasingly important both within a financial regulatory context and as a necessary prerequisite for the development of emerging capital markets. Using a comprehensive dataset of rating agencies and countries over the period 1989–1999, this paper demonstrates that artificial neural networks (ANN) represent a superior technology for calibrating and predicting sovereign ratings relative to ordered probit modelling, which has been considered by the previous literature to be the most successful econometric approach. ANN have been applied to classification problems with great success over a wide range of applications where there is an absence of a precise theoretical model to underpin the relationships in the data. The results for sovereign credit ratings presented here corroborate other researchers' findings that ANN are highly effective classifiers.     

An application of fuzzy sets to the Geological Strength Index (GSI) system used in rock engineering

Characterization of rock masses is one of the fundamental aspects of rock engineering. Particularly, as a rock mass characteristic, determination of the strength of closely jointed rock masses is difficult since the size of representative specimens including discontinuities is too large for laboratory testing. This difficulty can be overcome by using the Hoek–Brown empirical failure criterion in conjunction with the Geological Strength Index (GSI) Classification System. However, characterization of rock masses and determination of their strength may involve some uncertainties due to their complex nature. The fuzzy set theory is one of the tools to handle such uncertainties. This paper describes the application of fuzzy set theory to the GSI System by incorporating judgement and experience of practising engineers. For the purpose, the original GSI System and its modified form were defined by fuzzy sets, and Mamdani fuzzy algorithm was constructed using 22 “if–then” rules for evaluating discontinuity parameters and their ratings considered in the GSI System. In addition, slope instabilities in heavily jointed rock masses selected from two open pit mines in Turkey were back analysed and the results were evaluated to demonstrate and to check the performance of this approach.     

An interval arithmetic based fuzzy TOPSIS model

This work suggests a fuzzy TOPSIS model, where ratings of alternatives under criteria and importance weights of criteria are assessed in linguistic values represented by fuzzy numbers. Criteria can be categorized into benefit and cost. Ratings of alternatives versus criteria and the importance weights of criteria are normalized before multiplication. The membership function of each fuzzy weighted rating can be developed by interval arithmetic of fuzzy numbers. A ranking method can then be applied easily to develop positive and negative idea solutions in order to complete the fuzzy TOPSIS model. Finally, a numerical example demonstrates the feasibility of the proposed method.     

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.     

Constitutive models describing the influence of the geometry of partially-spanning joints on jointed rock mass strength: Regression and fuzzy logic analysis of experimental data

Using existing experimental data from Uniaxial Compressive Strength (UCS) testing, constitutive models were produced to describe the influence of joint geometry (joint location, trace length and orientation) on the UCS of rock containing partially-spanning joints. Separate approaches were used to develop two models: a multivariable regression model, and a fuzzy inference system model. Comparison of model predictions to the experimental data demonstrates that both models are capable of accurately describing the UCS of jointed rock with partially-spanning joints using information relating to joint geometry. However, according to the statistical evaluation methods used for performance evaluation, the multivariable regression model was significantly more accurate. Analysis of predictions made by the fuzzy inference system model showed that it was capable of resolving certain peculiarities in the influence of partially-spanning joint orientation on the compressive strength of rock that, from rock mechanics and fracture mechanics theory, should be expected. The multivariable regression model, whilst more accurate, did not recognise these peculiarities. Due to the additional insight that can be gleaned from the fuzzy inference system modelling, we recommend the use of the fuzzy inference system constitutive model in combination with the multivariable regression model.     

How good are fuzzy If-Then classifiers?

This paper gives some known theoretical results about fuzzy rule-based classifiers and offers a few new ones. The ability of Takagi-Sugeno-Kang (TSK) fuzzy classifiers to match exactly and to approximate classification boundaries is discussed. The lemma by Klawonn and Klement about the exact match of a classification boundary in R (2) is extended from monotonous to arbitrary functions. Equivalence between fuzzy rule-based and nonfuzzy classifiers (1-nn and Parzen) is outlined. We specify the conditions under which a class of fuzzy TSK classifiers turn into lookup tables. It is shown that if the rule base consists of all possible rules (all combinations of linguistic labels on the input features), the fuzzy TSK model is a lookup classifier with hyperbox cells, regardless of the type (shape) of the membership functions used. The question "why fuzzy?" is addressed in the light of these results.     

A parsimony fuzzy rule-based classifier using axiomatic fuzzy set theory and support vector machines

This paper proposes a classification method that is based on easily interpretable fuzzy rules and fully capitalizes on the two key technologies, namely pruning the outliers in the training data by SVMs (support vector machines), i.e., eliminating the influence of outliers on the learning process; finding a fuzzy set with sound linguistic interpretation to describe each class based on AFS (axiomatic fuzzy set) theory. Compared with other fuzzy rule-based methods, the proposed models are usually more compact and easily understandable for the users since each class is described by much fewer rules. The proposed method also comes with two other advantages, namely, each rule obtained from the proposed algorithm is simply a conjunction of some linguistic terms, there are no parameters that are required to be tuned. The proposed classification method is compared with the previously published fuzzy rule-based classifiers by testing them on 16 UCI data sets. The results show that the fuzzy rule-based classifier presented in this paper, offers a compact, understandable and accurate classification scheme. A balance is achieved between the interpretability and the accuracy.     

A fuzzy-logic-based approach for new product Go/NoGo decision at the front end

New product development (NPD) is both a complex process and a substantial business risk. It still requires 6.6 ideas to generate a successful product. Thus, researchers claim that inferior new products should be eliminated at the front end. Limited by both the nature and the timing of NPD, managers often perform screening in uncertain environments and based on incomplete information. Furthermore, the conventional evaluation approaches, which encapsulate or merely discard the ambiguity and multiplicity of possible concerns, make a screening economically sound but dysfunctional as well. Since most assessments are described subjectively by linguistic terms, a comprehensive method for new product screening using fuzzy logic is proposed, in which the criteria ratings and their corresponding importance are assessed in linguistic terms described by fuzzy numbers, and fuzzy weighted average is employed to aggregate these fuzzy numbers into a fuzzy-possible-success rating (FPSR) of the product. Finally, the FPSR is translated back into linguistic terms to derive at a new product screening decision. Furthermore, a case study is cited to illustrate the performance within an actual decision process. The result shows that this approach can efficiently aid managers dealing with ambiguity and complex environments in achieving relatively realistic and informative results, as well as give managers a high degree of flexibility in decision-making. In addition, the variations in linguistic values and levels of linguistic variables have an effect on the ranges of the FPSR which ultimately, affect the selection of the NPD project.     

Fuzzy-UCS: A Michigan-Style Learning Fuzzy-Classifier System for Supervised Learning

This paper presents Fuzzy-UCS, a Michigan-style learning fuzzy-classifier system specifically designed for supervised learning tasks. Fuzzy-UCS is inspired by UCS, an on-line accuracy-based learning classifier system. Fuzzy-UCS introduces a linguistic representation of the rules with the aim of evolving more readable rule sets, while maintaining similar performance and generalization capabilities to those presented by UCS. The behavior of Fuzzy-UCS is analyzed in detail from several perspectives. The granularity of the linguistic fuzzy representation to define complex decision boundaries is illustrated graphically, and the test performance obtained with different inference schemes is studied. Fuzzy-UCS is also compared with a large set of other fuzzy and nonfuzzy learners, demonstrating the competitiveness of its on-line architecture in terms of performance and interpretability. Finally, the paper shows the advantages obtained when Fuzzy-UCS is applied to learn fuzzy models from large volumes of data.     

考虑决策者权重和核心评级的模糊排序方法

决策者的专业背景、评价对象属性的受关注度均存在显著差异,而鲜有模糊多属性决策（Fuzzy Multiple Attribute Decision-making,FMAD）方法考虑决策者权重和属性核心评级对评价结果的作用,对此设计积分式模糊排序方法（Integral Fuzzy Ranking Method,IFRM）。在模糊理论的基础上,将语言变量量化为三角模糊数;根据个体评价与集结评价间的差距,更新决策者权重直至稳定;运用熵权法计算核心评级的信息熵,确定属性权重及评价对象的综合集结模糊评级,并基于积分式模糊偏好,给出任意两个方案间的偏好度,进而形成置信度最大的排序。以某品牌的共享单车为例,对比了常见多属性决策（Multi-Attribute Decision-making,MAD）方法的特点和方案排序结果,分析表明IFRM方案的排序结果有较高的一致性与置信度,对于解决模糊MAD问题具有可行性、有效性和优越性。     

Evaluating emergency response capacity by fuzzy AHP and 2-tuple fuzzy linguistic approach

Emergency management (EM) is a very important issue with various kinds of emergency events frequently taking place. One of the most important components of EM is to evaluate the emergency response capacity (ERC) of emergency department or emergency alternative. Because of time pressure, lack of experience and data, experts often evaluate the importance and the ratings of qualitative criteria in the form of linguistic variable. This paper presents a hybrid fuzzy method consisting fuzzy AHP and 2-tuple fuzzy linguistic approach to evaluate emergency response capacity. This study has been done in three stages. In the first stage we present a hierarchy of the evaluation index system for emergency response capacity. In the second stage we use fuzzy AHP to analyze the structure of the emergency response capacity evaluation problem. Using linguistic variables, pairwise comparisons for the evaluation criteria and sub-criteria are made to determine the weights of the criteria and sub-criteria. In the third stage, the ratings of sub-criteria are assessed in linguistic values represented by triangular fuzzy numbers to express the qualitative evaluation of experts’ subjective opinions, and the linguistic values are transformed into 2-tuples. Use the 2-tuple linguistic weighted average operator (LWAO) to compute the aggregated ratings of criteria and the overall emergency response capacity (OERC) of the emergency alternative. Finally, we demonstrate the validity and feasibility of the proposed hybrid fuzzy approach by means of comparing the emergency response capacity of three emergency alternatives.     

Estimation of elastic constant of rocks using an ANFIS approach

The engineering properties of the rocks have the most vital role in planning of rock excavation and construction for optimum utilization of earth resources with greater safety and least damage to surroundings. The design and construction of structure is influenced by physico-mechanical properties of rock mass. Young's modulus provides insight about the magnitude and characteristic of the rock mass deformation due to change in stress field. The determination of the Young's modulus in laboratory is very time consuming and costly. Therefore, basic rock properties like point load, density and water absorption have been used to predict the Young's modulus. Point load, density and water absorption can be easily determined in field as well as laboratory and are pertinent properties to characterize a rock mass. The artificial neural network (ANN), fuzzy inference system (FIS) and neuro fuzzy are promising techniques which have proven to be very reliable in recent years. In, present study, neuro fuzzy system is applied to predict the rock Young's modulus to overcome the limitation of ANN and fuzzy logic. Total 85 dataset were used for training the network and 10 dataset for testing and validation of network rules. The network performance indices correlation coefficient, mean absolute percentage error (MAPE), root mean square error (RMSE), and variance account for (VAF) are found to be 0.6643, 7.583, 6.799, and 91.95 respectively, which endow with high performance of predictive neuro-fuzzy system to make use for prediction of complex rock parameter.     

Ensemble Learning for Fetal Health Classification

: Cardiotocography (CTG) represents the fetus’s health inside the womb during labor. However, assessment of its readings can be a highly subjective process depending on the expertise of the obstetrician. Digital signals from fetal monitors acquire parameters (i.e., fetal heart rate, contractions, acceleration). Objective:: This paper aims to classify the CTG readings containing imbalanced healthy, suspected, and pathological fetus readings. Method:: We perform two sets of experiments. Firstly, we employ five classifiers: Random Forest (RF), Adaptive Boosting (AdaBoost), Categorical Boosting (CatBoost), Extreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LGBM) without over-sampling to classify CTG readings into three categories: healthy, suspected, and pathological. Secondly, we employ an ensemble of the above-described classifiers with the over-sampling method. We use a random over-sampling technique to balance CTG records to train the ensemble models. We use 3602 CTG readings to train the ensemble classifiers and 1201 records to evaluate them. The outcomes of these classifiers are then fed into the soft voting classifier to obtain the most accurate results. Results:: Each classifier evaluates accuracy, Precision, Recall, F1-scores, and Area Under the Receiver Operating Curve (AUROC) values. Results reveal that the XGBoost, LGBM, and CatBoost classifiers yielded 99% accuracy. Conclusion:: Using ensemble classifiers over a balanced CTG dataset improves the detection accuracy compared to the previous studies and our first experiment. A soft voting classifier then eliminates the weakness of one individual classifier to yield superior performance of the overall model.     

Type‐1 OWA Unbalanced Fuzzy Linguistic Aggregation Methodology: Application to Eurobonds Credit Risk Evaluation

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2‐tuple linguistic representation. However, the ordinal 2‐tuple linguistic approach does not exploit all advantages of Zadeh's fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the type‐1 ordered weighted average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modeled as unbalanced fuzzy linguistic labels.     

A generic fuzzy aggregation operator: rules extraction from and insertion into artificial neural networks

Multilayered feedforward artificial neural networks (ANNs) are black boxes. Several methods have been published to extract a fuzzy system from a network, where the input–output mapping of the fuzzy system is equivalent to the mapping of the ANN. These methods are generalized by means of a new fuzzy aggregation operator. It is defined by using the activation function of a network. This fact lets to choose among several standard aggregation operators. A method to extract fuzzy rules from ANNs is presented by using this new operator. The insertion of fuzzy knowledge with linguistic hedges into an ANN is also defined thanks to this operator.     

Tunneling Analyst: A 3D GIS extension for rock mass classification and fault zone analysis in tunneling

In this study, an extension called Tunneling Analyst (TA) has been developed in ArcScene 3D GIS software, part of the ArcGIS software package. It dramatically extends the functionalities of ArcScene because it allows: (1) estimation of the 3D distribution of rock mass rating (RMR) values using borehole and geophysical exploration data, (2) the modeling of 3D discontinuity planes such as faults from field-based structural measurements, and (3) analysis of 3D intersections and 3D buffer zones between proposed tunnel alignments and some discontinuities. Because TA can handle and visualize both 2D and 3D geological data in a single GIS environment, the tedious tasks required for data conversion between various software packages can be reduced significantly. The application to the Daecheong tunneling project in Korea shows that TA could present a rational solution to evaluating the rock mass classes along a proposed tunnel alignment and can also provide specific 3D spatial query tools to support the tunnel design work. This paper describes the concept and details of the development and implementation of TA.