Radial Basis Function to Predict the Maximum Surface Settlement Caused by EPB Shield Tunneling

Transcription

1 Radial Basis Function to Predict the Maximum Surface Settlement Caused by EPB Shield Tunneling M. Alizadeh Salteh, M. A. Ebrahimi Farsangi, R. Rahmannejad H. ezamabadi, ABSTRACT: This paper presents a method to predict the maximum surface settlement caused by EPB shield tunneling using Artificial eural etwork (A) based on Radial Basis Function (RBF). Maximum surface settlement above a tunnel due to a tunnel construction is predicted with the help of input variables. A MATLAB based radial basis network model is developed, trained and tested with data on ground deformation and shield operation which were collected through Bangkok MRTA project. The settlement is taken as a function of tunnel depth, distance from launching station, ground water level from tunnel invert, face pressure, penetration rate, pitching angle, tail void grouting pressure and percent tail void grout filling. The output variable is maximum surface settlement. Combining the extensive computerized database and knowledge of what influence the surface settlements, RBF can become a more useful predictive method compare to using Multi-Layer Perceptron (MLP) based network to predict the surface settlement. Key words: Radial Basis Function; EPB Tunneling; Settlement 1 ITRODUCTIO The work carried out in this paper is in relation with application of an artificial neural network based upon Radial Basis Function (RBF), to predict maximum surface settlement that is associated with MRTA project on Bankok city, Thailand. A lot of extensive work done base upon experimental formulations, and also using A [1],[4],[5],[6]. In the A work carried out, training errors, complicated structure and spending a lot of time were the main problems. Furthermore, the results obtained from A network had a lot of errors. In this paper, it is attempted Msc Student of Mining Engineering, Department of Mining Engineering, Shahid Bahonar University of Kerman, Kerman, Iran, mohammad_alizadeh2006@yahoo.com Assistant Professor of Mining Engineering, Department of Mining Engineering, Shahid Bahonar University of Kerman, Kerman, Iran, maebrahimi@mail.uk.ac.ir ; yahoo. co.uk Assistant Professor of Mining Engineering, Department of Mining Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. Assistant Professor of Electrical Engineering, Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. 1141

2 to solve the problem and minimize errors using RBF base network. The data used in this paper are adopted from previously study by Suchatvee, et al, The results obtained through RBF based network are compared to the results achieved by Suchatvee. 2 RBF ETWORKS 2.1 RBF etwork Structure RBF is a kind of artificial intelligence that simulates human's brain and nerve system with own structural instruments. One typical structure is made of two layers, radial network hidden layer and one linear output layer that surely with input layer it can be assumed 3 layers [2], which input nodes transfer input data to middle nodes that form hidden layer. Hidden nodes nonlinear response weighted and ultimate outputs of network will be computed in output layer [3], (Figure 1). Figure 1: Architecture of a RBF network One input vector X is used for the purpose of input in all of the RBF etworks, each with different parameters. Output of network is a linear combination of output from radial functions (Equation 1). ϕ( x) = i= 1 a ρ( x i c i ) in which is number of neurons in hidden layer, c i central vector for neuron i and a i are weights of linear output neuron. In the fundamental form, all inputs are connected to every hidden neuron. The norm is taken from Euclidean distance and main function is Gaussian function (Equation 2) [3]. 2 ρ( x ci α exp[ β ( x c i ]. (2) Main function, Gaussian, is locally in the form of lim ρ( x ci x (1) (3) 1142

3 that varies parameters in one neuron that has a little effect on input quantities that are distanced from center of that neuron. RBF networks are global approximators on compact subset of R n. It means that one RBF network with sufficient hidden neurons can approximate every continuous function with elective accuracy. The weights of, a i c i and β are modified in treatment that is optimized fit between φ and data. 2.2 Training method of RBF network In one RBF network there are three kinds of parameters that need to be chosen because of adjusting network to a special task: the central vectors c i, the output weights w i and transversal parameters β i. In the next step of training the weights are adjusted as data currents at every time step. For some of tasks, it is felt that a target function should be defined and parameter values chosen, that minimizes its value. Most common target function is minimum squares function (Equation 4) [3]. K( w) that def = t= 1 def K ( w) t [ y( t) ϕ( x( t), )] 2 K ( w) = w t It is expressly seemed dependence in weights. Squares minimum function can be minimized by optimum select of weights to optimize accuracy of fit. Some times there are many targets: for example smoothness as well as accuracy must be optimized. In this situation it is useful to optimize the trimmed target function. 3 FACTORS AFFECTIG SETTLEMET Factors affecting settlement are: tunnel geometry, geology condition and boring machine factors [1]. Every of these factors consist of parameters, which are used for inputs of network. Geometry factor contains two parameters, depth and distance from available station and another factor that affects on surface settlement is tunnel diameter. Geology conditions were avoided due to little effects on settlement. Boring machine (shield) parameters are face pressure, penetration rate and pitching angle and other effective parameters are tunnel bottom distance from under ground water and grouting pressure and grout filling percent [1]. 4 OPTIMIZATIO OF RBF ETWORK MODEL etwork model in this study contains inputs such as depth, distance from available station, and tunnel bottom distance from under ground water, penetration rate, pitching angle, grouting pressure and grout filling percent [1]. Model output is maximum settlement of surface. umbers of data sets used are 49 consisting of 8 inputs. The range for inputs and output are shown in Table 1. Data devise to 3 part: training data, test data and credit data. 90% of data are used for training and 10% are (4) (5) 1143

4 used for credit. Once again training data devise to 80% for training and 20% for test. To create a good network model that can explicitly predict all of the new data, it is necessary that an optimal network model be created. For this purpose, a trial and error approach is used. One network model is created while proper value of radial basis functions spread is found at network to have minimum error. Possible variables in the of trial and error process are 1) value of spread of radial basis function 2) network structure. Table 1. Ranges of the data used for the RBF model inputs and output [1] Input variables Minimum value Maximum value Depth (m) Distance from shaft (m) Invert to WT (m) Average face pressure(bar) Average penetration Pitching ( ) Grouting pressure (bar) % Grout Soft filling Measured settlement (mm) With various spread of radial basis function, network is learned until reaching to proper spread of radial basis function. After training, credit data will be tested then network output will be attained. After that, its value will be compared with real data. If the difference between them is small, it shows that this network is useful and applicable. By performing this process, the network with least difference is chosen as optimal network. For determining error in network Root Mean Squared Errors (RSME) and Mean Absolute Errors (MAE) were used [1], [4]. Root mean square errors are defined by: RMSE i = = 1 2 ( o t ) i i and mean absolute errors are defined by: = MAE = ( ( o ti ) i i ) 1 in which O is predicted settlement value by network and t is real settlement value in the field. With minimum RMSE and MAE values corresponding to the network, the network is optimum. 5 RBF MODEL TO PREDICT SURFACE SETTLEMET In this part, network is trained by data adopted from [1]. Results show that network can be fitted with measurable data and then can be tested with credit sample. Optimum network have minimum RMSE. Both results of training and test are shown in Figure 2. Model performance is summarized in Table 2. (6) (7) 1144

5 Table Figure 2. Predicted settlement versus measured settlement using RBF network Figure 3. Predicted settlement versus measured settlement using MLP network A comparison is made between RBF & MLP models. Table 3 shows that RBF model provides more accurate settlement prediction than MLP model. 1145

6 Table2: Performance of the optimal RBF model Data set Training Test Credit ( mm) RMSE 4.23e ( mm) MAE 1.09e Table3: Performance of RBF and MLP models for credit data sets Performance measure RMSE MAE RBF MLP COCLUSIOS To minimize tunneling project costs and their settlement risk as a result of ground movements, the engineers need to predict settlement in tunnels accurately for which experimental methods are weak. Recently, neural networks widely used in prediction of surface settlement. Based on the results obtained in this study, it can be concluded that RBF based model network, due to having a simpler structure, compare to a MLP network, can predict surface settlement with more accuracy. REFERECE [1] Suchatvee S.; Herbert H. E; (2006) Artificial neural networks for predicting the maximum surface settlement caused by EPB shield tunneling Tunneling and Underground Space Technology 21. [2] Sarimveis H.; Doganis P.; Alexandridis A.; (2006) A classification technique based on radial basis function neural networks Advances in Engineering Software 37, [3] Moody J.; Darken C. J.; (1989) Fast learning in networks of locally tuned processing units eural Computation, 1, [4] Shahin M. A.; Jaksa M. B.; Maier H. R. (2002) Artificial neural networks based settlement prediction formula for shallow foundation on granular soils Australian Geomechanics. [5] eaupane K.M.; Adhikari.R.; (2006) Prediction of tunneling-induced ground movement with the multi-layer perceptron Tunneling and Underground Space Technology 21, [6] Benardos A.G.; Kaliampakos D.C.; (2004) Modelling TBM performance with artificial neural networks Tunnelling and Underground Space Technology 19,