ATS11-03520 A fuzzy logic model to predict the performance of hard rock tunnel boring machine Mansour Hedayatzadeh 1, Kourosh Shahriar 2, Jafar Khademi Hamidi 2 1 Mining Engineering Group, Islamic Azad University, Tehran South Branch, Iran 2 Departments of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran ABSTRACT Prediction of tunnel boring machine (TBM) is one of the most crucial and decisive issues in underground excavation projects. Precise estimation of machine performance can significantly mitigate the capital costs of mechanical excavation project. The main objective of this study is to estimate the TBM penetration rate by constructing a fuzzy inference system analysis. For this purpose, rule-based (Mamdani model) fuzzy logic were employed to build a fuzzy model and 34 TBM field datasets including Q rock mass classification system, rock material properties and machine characteristics along the route of the tunnel were compiled. Hence, the F Q (fabric index of Q rock mass classification system), F f (the ratio of uniaxial compressive strength and load per cutter) and Fα were determined as input parameters In order to verify the validity of the two models, the predicted penetration rate and the measured penetration rate gained from the field records were compared. Results picked out form this predictor model revealed that this model has a strong capability for estimation of TBM performance with a correlation coefficient of 81.5%.. KEYWORDS Keywords: Tunnel boring machine; rate of penetration (PR); advance rate (AR); fuzzy inference system; rock mass classification system. 1. INTRODUCTION Performance prediction of tunnel boring machine is one of the engineering geological problems that commonly have complexity and ambiguity. This issue is crucial because a precise estimation of machine performance can considerably influence the capital costs of mechanical excavation project. Performance prediction of TBM strictly relies on the estimation of the rate of penetration (PR), defined as the ratio of excavated distance to the operating time during continuous excavation phase, and advance rate (AR), the ratio of both mined and supported actual distance to the total time. To date, many attempts were made for the development of the accurate prediction models [1-10]. In addition to these models in recent years some prediction models have been developed using artificial intelligences including artificial neural network (ANN), fuzzy logic and Neuro-Fuzzy hybrid techniques [11-20]. Taking into consideration the nature of problem, the main purpose of the present study is to develop a model by utilizing the fuzzy logic for predicting TBM performance. In order to achieve this aim, a database composed of rock mass properties such as fabric indices of four rock mass classification and the angle between plane of weakness and tunnel axis, intact rock properties including uniaxial compressive strength, machine specification including net thrust per cutter together with actual measured TBM penetration rate, was compiled along the 6.5 km bored Alborz service tunnel.
2. PROJECT DESCRIPTION AND GEOLOGY OF THE STUDY AREA The Alborz service tunnel is the longest tunnel section (6.5 km) along Tehran-Shomal Freeway, situated in the high elevation portions of Alborz Mountain Range, connecting the capital city of Tehran to the Caspian Sea in the North (Figure. 1). The service tunnel as a pilot tunnel with a diameter of 5.20 m was excavated by an open gripper TBM in advance of two main tunnel tubes to be excavated subsequently. The purpose of the service tunnel is to carry out site investigations, drainage of the rock mass, providing access for main tunnel excavations and service, ventilation and drainage during operation of the complete tunnel system. 3. 1. ROCK MATERIAL PROPERTIES Intact rock strength (Uniaxial compressive strength, Brazilian tensile strength, Point load index, etc.) Toughness (Punch penetration index, Fracture toughness index) Hardness and drillability (Siever s J-value, Total and Taber hardness indices, Schmidt hammer hardness) Brittleness (Swedish brittleness S 20, brittle indices (BI 1 = σ c / σ t and BI 2 = [(σ c - σ t ) / (σ c + σ t )] where σ c and σ t are uniaxial compressive and tensile strengths of intact rock, respectively) Abrasiveness indices (Cerchar Abrasivity Index CAI and Abrasion Value AV ) Others parameters such as (Poisson ratio, Elasticity module, internal friction angle, Porosity, Grain size, etc.) 3. 2. ROCK MASS PROPERTIES GSI rock mass classification system which indicates rock mass properties RMR rock mass rating classification system defined Figure. 1 Geographical location of Alborz tunnel Site investigation for the service tunnel included a geological surface mapping, a geophysical investigation along the alignment from the surface and some index laboratory tests on rock samples. Based on the results of geological site investigations, the main lithological units through which the tunnel was driven consist of sandstone, tuff, gypsum, shale and limestone layers (Figure. 2). as, where, R 1 is the rating for intact rock strength, R 2 is the rating for RQD, R 3 is the rating for discontinuity spacing, R 4 is the rating for discontinuity conditions, R 5 is the rating for ground water, and R 6 is the rating for discontinuity orientation. The rock mass properties could be defined as R 2 +R 3 +R 4 in RMR system [3]. In Q rock mass classification system, Q = ( RQD/J n ). (J r /J a ).)J w /SRF). The rock mass properties are considered as (RQD/J n ). (J r /J a ) [2]. In RMi classification system, RMi = σ ci * JP the rock mass properties could be determined as Jp that related to Jv (volumetric joint count), V b the block volume (m 3 ), L (the mean block diameter ), S (spacing of joints within a set) and jc (the joint conditions rating) [14]. 3. 3. ROCK MASS CONDITIONS Figure. 2 Longitudinal geological profile of Alborz service tunnel 3. PARAMETERS AFFECTING THE TUNNEL BORING MACHINE PERFORMANCE There are many factors affecting the TBM performance such as rock material, rock mass parameters, machine characteristics and operational parameters. The following list gives an overview of variables that are taken into account as potential inputs to the prediction model: Joint condition, joint orientation such as R 6, the partial rating for the adjustment of discontinuity orientation in RMR system, and the angle between the tunnel axis and the planes of weakness In-situ stress status, such as SRF, the stress reduction factor, in Q system, σ v and σ h (in situ stress condition) Groundwater conditions such as R 5 parameter, the rating for groundwater, in RMR system and J w parameter, the factor for joint water pressure or inflow, in Q classification system. 3.4. MACHINE CHARACTERISTICS Thrust (cutter load)
Torque RPM (Rotation per Minute) Power Disc specifications including number and spacing of disc cutters on the cutterhead, disc geometrical specifications such as diameter, tip width and angle of tip, and disc mechanical specifications such as maximum load capacity, allowable velocity. Knowledge about the relationships among some of these factors and their effect on the TBM performance are available from the previous researches [8, 7, 9]. These experiences were the primary source of information for designing the rule bases of the fuzzy model. The reasoning behind the choice of the most related factors and the translation of the expert knowledge into the fuzzy if-then rules is described in detail in Section 5. Numerical measurements from field observations of 34 tunnel sections were used to validate the model. 4. THE FUZZY MODEL In order to predict the performance of TBM based on the data set compiled along the route of tunnel, a fuzzy logic model was developed. Generally, the construction of the fuzzy model has several steps that are illustrated in Figure 5. More detailed information about these steps including, selection of related input variables, and design of the membership functions, translation of the expert knowledge into if-then rules and determination of defuzzification method are given in this section. Operation of Fuzzy system Crisp input Fuzzification Fuzzy input Rule evaluation Fuzzy output Defuzzification Crisp output Figure. 3 Description of operation system 5. FUZZY LOGIC METHOD Input function Rules/Inference Output membership function The fuzzy logic advantage in comparison with traditional methods, such as statistics, is the capability of this model to describe complex and nonlinear multivariable problems that have an ambiguity and complexity [23]. Many researchers have satisfyingly used the fuzzy approach in the engineering geology. The Mamdani, the Tagaki-Sugeno-Kang, the Tsukamoto and the singleton fuzzy are the popular models wildly applied in all aspect of engineering. However, the Mamdani fuzzy algorithm is the most appropriate fuzzy method employed in engineering geological problems [25]. Generally, a fuzzy model is constructed by expert opinion in the form of linguistic rules. In a classical set, an element belongs to, or does not belong to, a set. Because fuzzy sets describe vague concepts based on the premise that the elements used are not numbers but belong to words or the value of a linguistic variable, an element of a fuzzy set naturally belongs to the set with membership values from the interval [0, 1]. 5.1. Fuzzy logic model to predict rate of penetration of tunnel boring machine 5.1.1. Determination of input variables As mentioned previously, many different factors affect the TBM performance, but not all of them are exerted in the fuzzy model. Some of these variables are not included because the knowledge about their influence is still insufficient and the experts consider them of a minor importance. Considering the above mentioned issues and based upon existing facilities in the site, an attempt is made to consider some of these parameters for predicting TBM penetration rate in this study. Among the rock material characteristics, UCS was selected in the model, because it could be measured simply and relatively represents intact rock property. Also, cutter load was selected as a machine parameter in the model. Rock mass properties can be extracted form part of the Q, RMR, RMi and GSI classification systems. Among these systems, the fabric index of Q system (F Q ), which is defined as (RQD/J n ).(J r /J a ) was selected. Hence, three distinct parameters were finally taken into account to construct the fuzzy logic model for TBM penetration rate considering all influencing parameters on TBM performance as the followings: - F Q that is representative of rock mass properties - F f as the ratio UCS/F, represents intact rock characteristic and machine specifications - F α = log ArcSin (Sin α f * Sin (α t α s )) that demonstrates the rock mass condition. α f and α s are dip and strike of encountered planes of discontinuities in rock mass, and α t is the direction of the tunnel axis in degrees[14]. Descriptive statistical distribution of mentioned variables in the database and input parameters for developed model is summarized in Table 1. Influence of each variable in obtained model has been investigated by performing multiple linear regression analysis. Table 1.descriptive statistics of generated database Variables N Min. Max. Mean Variance F Q 34 0.08 23.90 8.26 28.79 F f (MPa/tonf) 34 1.98 5.80 4.49 0.982 F alpha (degree) 34 8.00 83.0 39.41 381.93 PR (m/h) 34 2.85 5.30 3.93 0.535 Figures 4-6 illustrate the correlations between the individual independent variables and the actual measured ROP. The
Figures also, include the coefficients of correlation (R 2 ) which is an indicator of correlation strength. As illustrated in Figure 7, to set up input and output variables in the MATLAB environment, fuzzy inference system (FIS) editor was implemented. Both input and output variables were fuzzified with membership function graphically designed with a MATLAB toolbox. The fuzzy membership function defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1. Both input and output variables were fuzzy proposition in Mamdani model. 5.1.2 Fuzzification of input and output variables and selection of membership function Figure.4 Relation between measured PR and F f Figure.5 Relation between measured PR and F Q In construction of a fuzzy model, the use of the proper membership function (MF) is a critical and crucial issue because MFs express the fuzziness of the models variables. There are many suggestions on how to build the appropriate MF for a particular model. Ross [22] describes seven procedures for this task (i.e. Intuition, inference, rank ordering, angular fuzzy sets, neural networks genetic algorithms, and inductive reasoning). Tsoukalas and Uhrig [23] add the use of statistical data as a method to determine an MF. Liberatore [24] also adopts a similar approach in an application for assessing project schedule. Advantage of MFs is that they can be produced based on subjective judgment and intuition especially in cases where there is a lack of data. The shape of the membership function of fuzzy sets can be either linear (trapezoidal or triangular) or various forms of nonlinear, depending on the nature of the system being studied. In this paper the triangular membership function is selected among a set of functions that the FLT provides, including the trapezoidal, the generalized bell-shaped, Gaussian, Sigmoidal, and polynominal MFs. Triangular MF is selected because it presents the following characteristics[24]: A. it is simple to understand and handle B. it is computationally affordable. Figure 6. Relation between measured PR and F α With considering the good relationship between Ff, FQ and Fα with PR, To predict ROP, three parameter including F Q, F f and F α could be used as input parameters that they were gained from 34 sections of Alborz tunnel. 0, x< a MD A (x) = (x-a)/ (b-a) a x < b (1) (c-x)/(c-b) b x < c 0, x> c MD A (x) is the membership function of a fuzzy set; a, b, c are the constant. In this study for construction and determination of the membership function parameters, the statistical method, considering the performed statistical analysis, were utilized. Hence, the first input, F Q, had five member functions: min, min-med, med, med-max and max with respect to the range of F Q, which is ranged from 0.8 to 24. Figure. 8 presents the shape and range of each membership function for this input. Figure. 7 Determination of input and output parameters
5.1.3 Description of If Then rules Figure. 8 Membership function of the PR input parameter, F Q The F f as the second parameter had three membership functions which are min, med and max. It varies from 1.8 to 5.9 MPa/tonf and the shape and range of its membership functions are shown in Figure. 9. Figure. 9 Membership function of the PR input parameter, F f F α was taken into account as the third parameter ranging between 9 and 79 degrees, has five membership functions including min, min-med, med, med-max, max. Figure. 10 demonstrates the shape and range of membership function of F α parameter. Figure. 10 Membership function of the PR input parameter, F α The penetration rate (PR) was considered as the output parameter that varies from 2.2 to 5.3 m/h. The shape and range of each membership function of the output are illustrated in Figure. 11 Figure. 11 Membership function of the PR input parameters (1) Input output relationship by fuzzy conditional rules is a significant concept in fuzzy logic. A fuzzy conditional rule is generally composed of a premise and a consequent part (IF premise THEN consequent), for example, if the level1 is high, then level2 is low, where the terms high and low can be represented by fuzzy sets or more specifically by membership functions. Zadeh introduced the inference mechanism of fuzzy logic reasoning, which is based on the compositional rule of inference [25]. By using this inference mechanism, an output set is obtained given the rules and the input variables. The Mamdani algorithm is one of the most common algorithms used in fuzzy logic. Mamdani and Assilian showed that the concepts of fuzzy sets and fuzzy logic can translate an entirely unstructured set of linguistic heuristics into an algorithm [23]. This algorithm is one of the most used fuzzy methods to apply in complex engineering geological problems, since most geological processes are defined with linguistic variables or simple vague predicates. The Mamdani fuzzy algorithm takes the following form: If X I is A ii... and X r is A ir then Y is B i for I = 1, 2,..., K (2) X I, X r : Input variables A ii, A ir, B i : Linguistic terms (fuzzy sets) Y: Output variables, K: number of rules In the Mamdani fuzzy model, different fuzzy set operators, such as and, or and not, can be used to combine the premise propositions of the rules. In this algorithm, the contribution of each rule to the output of the model is a fuzzy set. The inference reasoning mechanism in the Mamdani fuzzy model is based on the compositional rule of inference. To perform inference in a rule based fuzzy model, the fuzzy proposition needs to be represented by an implication function. The implication function is called a fuzzy if then rule or a fuzzy conditional statement. The general form of fuzzy if then rule is as follows: If X is A then Y is B Where A and B are linguistic values represented by fuzzy sets. The use of fuzzy set provides the generalization of the information used to describe the behavior system. The if-part of the rule is called premise and the then-part of the rule is called consequence. Generally 34 rules with combining of input membership functions (premise part) to output membership functions (consequent part) were utilized in the model.some of the rules are as follows: 1. IF(FQ is MINMED)AND(Ff is MED)AND(Falpha isminmed)then(pr is MEDMAX) 2. IF(FQ is MINMED)AND(Ff is MED)AND(Falpha is MAX)THEN(PR is MED) 3. IF(FQ is MIN)AND(Ff is MIN)AND(Falpha is
MEDMAX)THEN(PR is MAX) 4. IF(FQ is MIN)AND(Ff is MIN)AND(Falpha is MEDMAX)THEN(ROP is MEDMAX) 5. IF(FQ is MIN)AND(Ff is MED)AND(Falpha is MINMED)THEN(PR is MEDMAX) 6. IF(FQ is MINMED)AND(Ff is MED)AND(Falpha is MEDMAX)THEN(PR is MED) 5.1.4 Selection of defuzzification method There are several different ways to define the result of a rule, but one of the most common and simplest is the "max-min" inference method, in which the output membership function is given the truth value generated by the premise. Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are "defuzzified" to a crisp value by one of the several existing methods. There are dozens in theory, each with various advantages and drawbacks. The "centroid" method is very popular, in which the "center of mass" of the result provides the crisp value. The example below demonstrates max-min inferencing and centroid defuzzification for a system with input variables "x", "y", and "z" and an output variable "n". Note that "mu" is standard fuzzy-logic nomenclature for "truth value": Fig. 13, when input parameters are F Q =6.1, F f =3.23 MPa/tonf, and F alpha =55 degrees, ROP of 4.27 m/h is predicted. To assess the validation of the model, the actual values of ROPs from the 34 sections in the field were compared with predicted values from fuzzy model as illustrated in Fig. 13. The figure shows that the predicted values are in a good agreement with actual ROPs (R 2 = 0.815). Hence, the fuzzy model also has a strong capability to predict the penetration rate of TBM. Fig. 13 Correlation between measured and predicted ROPs Fig. 12 Centriod of area defuzzification technique[24]. In this study the centeriod method was employed because of its simplicity and popularity that calculated the centroid of the area under the membership function as: z * COA = (z) z dz A * Z COA (z)dz A Where is the crisp value for the "z" output and A(z) is the aggregated output membership function. 5.1.5 Result of developed fuzzy model In this part of study to access the estimation of TBM penetration rate, Mamdani model was performed. This model is capable to predict PR using input variable conditions, since it can interpolate input parameters. For instance, as illustrated in (3) 3. CONCLUSIONS A fuzzy model has been developed for the prediction of hard rock TBM penetration rate based on expert knowledge, experience, and data obtained from 34 sections along the route of Alborz service tunnel. In order to predict TBM ROPs, three input variables including fabric index of Q classification system, uniaxial compressive strength of intact rock, cutter load and the angle between tunnel axis and discontinuity planes were utilized. Results obtained from fuzzy model showed that it has a stronger capability to predict penetration rate, with correlation coefficient of 0.815. However, the range of the input data used for development of the proposed prediction model were very limited and as such, the results cannot be considered to be universal and more in depth study is required to extend the finding of this study to develop a universal model. REFERENCES [1] Bamford, W.F. 1984. Rock test indices are being successfully correlated with tunnel boring machine performance. Proc. 5 th Australian Tunneling Conference, Vol. 2, 9-22. [2] Barton, N. 2000. TBM tunneling in jointed and faulted rock. Rotterdam: Balkema, Brookfield, p. 173. [3] Bieniawski, Z.T., Tamames, B.C., Fernandez, J.M.G., Hernandez, M.A. 2006. Rock Mass Excavability (RME) Indicator: new way to selecting the optimum tunnel construction method, ITA-AITES World Tunnel Congress & 32nd ITA General Assembly, Seoul. [4] Blindheim, O.T. 1979. Boreability predictions for tunneling. PhD Thesis, The Norwegian Institute of Technology, p. 406. [5] Bruland, A. 1998. Hard rock tunnel boring. PhD Thesis, Norwegian University of Science and Technology, Trondheim. [6] Cassinelli, F., Cina, S., Innaurato, N., Mancini, R., Sampaolo, A. 1982. Power consumption and metal wear in tunnel-boring machines: analysis of tunnel-boring operation in hard rock. Tunnelling 82, Inst.
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