Artificial Intelligence Techniques

By: Rohit Singh Kaushal Branch: Electronics (R.K.D.F.I.S.T., Bhopal) Email: [email protected] & Saurabh Saxena Branch: Computer Science (L.N.C.T, Bhopal) Email: [email protected]

Artificial Intelligence Techniques for the Design and Analysis of Deep Foundations By : Rohit Singh Kaushal Saurabh Saxena

INTRODUCTION Presently, there are numerous approaches for the prediction of the axial load-bearing capacity of driven piles as well as for laterally loaded drilled shafts. Most of these methods either oversimplify the nature of the problem or improperly consider the effect of certain governing factors. The problem is extremely complex owing to the large number of uncertain parameters that affect the behaviour of piles. Neural Network approach is one alternative that is capable of incorporating the uncertainties associated with the controlling parameters.

Numerous investigators have approached the problem by considering the correlation with in situ tests such as the standard penetration test, the cone penetration test, and the pressurementer. Although these tests reflect, to some extent the natural subsurface conditions, they suffer much inherent variability. Many empirical formulas have been developed between soil parameters and pile capacity in both end-bearing and friction piles, based on load test results to provide quick estimate of the axial pile capacity. Mostly these procedures do not provide design guidelines that are consistent with the physical processes that dictate actual pile capacity. In the case of the design of laterally loaded piles, current methods are rested upon the non-linear load –deflection analytical techniques using the p-y curves, which are based upon an interpretation and empirical evaluations of few lateral load tests. These analytical expressions include a considerable degree of empiricism. Obtaining the lateral load capacity of piles from knowledge of soil properties will require consideration of both local soil-shear behavior and the three-dimensional soil displacements due to the pilepressure distribution. The deflection of the pile is dependent on the soil response and the soil reaction is a function of the pile deflection. Thus, the problem has to be cast in an iterative solution algorithm to ensure compatibility of displacement and static equilibrium. Laterally Loaded Pile Laterally loaded piles occur frequently in the support of bridge abutments, retaining walls, overhead signs, noise barrier walls, in stabilizing man-made embankments and natural slopes, offshore structures etc. Though they represent the common situation and not the exception in deep foundations, there is a scarcity of simple reliable approaches for the design and analysis of laterally loaded pile. The behavior of a laterally loaded pile depends on the properties of both the soil and the foundation structure. Applied lateral load induces flexural stresses in the pile. In response to these stresses the

foundation moves laterally and thus mobilizes resisting forces in soils. The lateral soil resistance per unit length of the pile is denoted by p. The magnitude of p increases as the lateral deflection (y) increases and eventually reaches a peak value pult as illustrated graphically in figure 1.

Figure 1. Soil reaction per unit length (p) as a function of the lateral deformation (y) Relevant foundation properties that govern the behavior of the pile include: diameter (D), length (L), modulus of elasticity (E), and moment of inertia (I). The soil properties are implicit in the p-y curve and include, for instance, the soil type, confining stress, coefficient of friction between soil and pile, and others.

Currently, the design of laterally loaded piles is rested upon the non-linear load–deflection analytical techniques using the p-y curves, which are based upon an interpretation and empirical evaluations of few lateral load tests. It models the soil as a series of non-linear springs as depicted in figure 2. These analytical expressions include a considerable degree of empiricism.

Figure 2. The p-y method: The load-deflection behavior of each spring is defined by its p-y curve.

Obtaining the lateral load capacity of piles from knowledge of soil properties will require consideration of

both local soil-shear behavior and the 3D soil displacements due to the pile-pressure distribution. This is further complicated by variation in the soil stiffness with the different planes of deformation due to soil anisotropy. Thus, the problem cannot be solved by the equations of static equilibrium alone. Hence, a design method that fulfils validity, simplicity, and reliability, is needed within the framework of laterally loaded piles design. In this research Neural Network models are proposed as an alternative approach that encompass to a greater extend the stated requirements. Axially Loaded Pile For the prediction of the axial pile bearing capacity, there are many approaches. Each method has its benefits and drawbacks and none is universally accepted. Therefore designers often use more than one method and base the final design on a synthesis of the results. At the present time, the question about solution uniqueness still remains unresolved. The approaches to estimate the axial load pile capacity are generally grouped into three broad categories: •

(a) Full-scale load tests.

• (b) Analysis based on soil properties obtained from laboratory or in-situ tests. These are known as static methods. •

(c) Analysis based on pile driving dynamics, known as the dynamic method.

A reliable design will usually be attained based on the results from approach (a). However, static load tests are costly and time consuming. In approach (b) the efficiency of pile-static formulas has been found to be questionable and correlate poorly with the static load test. The procedures in (c) make use of the pile-soil

dynamic interaction model and apply the stress-wave matching techniques. In this group, the most difficult part is the definition of the soil-pile interface models, which are largely empirical. The problem of determining the pile capacity from simple soil tests like SPT- N values is of a great interest in pile engineering. It has attracted many researchers over decades resulting in different solutions, known as pile driving formulas. Because of the complexity and the uncertainty associated with geo-technical media, no satisfactory solution or general procedure for the estimation of the pile capacity from simple soil tests is available. The main problem with the pile driving formulas is that the physical laws used to define them oversimplify the carrying behavior of driven piles. However, it is clear that certain relationship exists between the parameters involved in these formulas and the pile bearing capacity. The complexities of the problem along with the uncertainty associated with the multivariate and intrinsically noisy data render the problem ideally suited for solution by neural network methodology.

NEURAL NETWORK APPROACH The human brain is made up of a web of billion cells called neurons, and understanding its complexities is seen as one of the last frontiers in scientific research it the aim of AI researchers to construct electronic circuits that act as neurons do in the human brain. The complex network of neurons is what gives humans intelligent characteristics. By itself, a neuron is not intelligent, but when grouped together, neurons are able to pass electrical signals through networks. This was one of the major concepts behind the development of neural systems.

Recently it is being suggested that artificial neural networks can acts as model for the prediction of the behavior of axially loaded piles, using dynamic stress-wave data. The main objective is to develop optimal models using only simple input data. These data include SPT-N values and the geometrical properties. The models involved are Backpropagation, and Generalized Regression Neural Networks. Neural Network Anatomy Artificial neural networks are nonmodel-based pattern recognition and approximation methods. They are also known to be noise tolerant; they are adaptive and they can learn and generalize. Backpropagation neural networks have been recently used in the prediction of the axial pile capacity. No attempts so far have been made to apply neural network methods to determine the lateral load capacity of piles. The network architecture affects the optimal training and its ability to generalize. The general criterion in designing neural networks is to start from the simplest structure that can provide the essential consistency and adequacy. In this study, varieties of neural network models are introduced for the design of laterally

loaded piles. Namely, Feed forward Backpropagation, and Generalized Regression Networks are implemented. It also addresses the data preparation and data inception along with the problems involved with the artificial neural networks. Following is a short description of these architectures. Backpropagation Neural Networks (BPNN) BPNN are the most widely used type of artificial neural networks. Typically BPNN consists of many simple processing elements called neurons grouped in layers and connected by interconnections called synapses. Figure 3 illustrates a three-layer feedforward neural network.

Figure 3. Typical Feedforward Backpropagation Neural Network

Presently, there are many variations of the back propagation algorithms. In this study, Resilient Backpropagation training is being adopted. The main advantage of the Resilient Backpropagation training

algorithm is the elimination of the harmful effects of the Gradient methods (partial derivative problems when using the sigmoid transfer function). The Resilient Backpropagation is also characterized as simple batch mode training algorithm with fast convergence and minimal storage requirements. In this study, a three-layer and four-layer feedforward backpropagation networks were investigated. Choosing an appropriate number of hidden neurons is extremely important aspect in the backpropagation networks. However, there is no exact method for determining the number of hidden layer neurons. Using too many will increase the training time and may cause the overfitting problem (memorising the training pattern rather than generalizing the prediction). On the other hand, using fewer hidden neurons often increased the likelihood of learning algorithm becoming trapped in a local minimum. Thus, it is imperative that we use absolute minimum number of hidden neurons, which will perform adequately. One rough guideline for choosing the number of hidden neurons in many problems is the geometric pyramid rule. It states that, for many practical networks, the number of neurons follows a pyramid shape, with the number decreasing from the input toward output. The number of neurons in each layer follows a geometric progression. Other investigators suggested that the nodes on the hidden layer should be between the average and the sum of the nodes on the input and output layers. These are only rough approximations to the ideal hidden layer size. The best approach to find the optimal number of hidden neurons is to start with a few numbers of neurons, then slightly increase the number of hidden neurons, until no significant improvement is noted. The results of this approach reveal: •

No. of neurons in the first hidden layer = 10

•

No. of neurons in the second hidden layer = 6

•

No. of neurons in the third hidden layer = 3

A variety of different transfer functions were investigated to achieve best performance in training as well as in testing. Generalized Regression Neural Networks (GRNN) The generalized regression neural network (GRNN) is a feedforward neural network based on non-linear regression theory consisting of four layers: the input layer, the pattern layer, the summation layer, and the output layer (see Figure 4). While the neurons in the first three layers are fully connected, each output neurons is connected only to some processing units in the summation layer. The individual pattern units compute their activation using a radial basis function, which is typically the Gaussian kernel function. The radial basis function has a maximum of 1 when its input is 0. As the distance between the input vector and the weight vector decreases, the output increases. Thus the radial basis neuron acts as a detector, which produced 1 whenever the input is identical to its weight vector. The summation layer has two different types of processing: the summation units and a single division unit. The number of the summation units is always the same as the number of the GRNN output units. The division units only sum the weighted activation of the pattern units without using any activation function. The training of the GRNN is quite different from the training used for the BPNN. It is completed after presentation of each input-output vector pair from the training set to the GRNN input layer only once; that is, both the centers of the radial basis functions of the pattern units and the weights in connections of the pattern units and the processing units in the summation layer are assigned simultaneously. The training of the pattern units is unsupervised, but employs a special clustering algorithm, which makes it unnecessary to define the number of pattern units in advance. Instead, it is the radius of the clusters that needs to be specified before the training starts.

Figure 4. General Regression Neural Network Diagram DATABASE The database covers a wide spectrum of variation in soil formations, stress history, geographic locations, pile types, length and diameters. The basic types include steel pipe piles, steel H-piles, prestressed concrete piles, and precast concrete piles. DATA PREPROCESSING Database preparation for the training of the neural network represents a crucial step in the neural network

modeling. The performance of the network model rests solely upon the input training pattern. The best source of the input training pattern in complex phenomenon like the soil-structure interaction in laterally loaded piles, is an experimental investigation in which a large number of cases are properly tested. The measured data depicts the inputs and outputs variables for the training of the neural network. These data are then divided up into training and testing subsets. The training subset constitutes 60% of the database whereas the testing 40%. The development of the training network starts with the selection of a number of different combinations of input variables to evaluate the most reliable neural network model. Then, about 20% of the patterns in the training set is extracted before training and used for the cross validation to satisfy the adequacy of the generalization of the proposed neural network paradigms. For the pre-processing phase, all input and output data are normalized to values between 0-1. The scaling is performed in accordance with the probability approach. The method is described by the following equations: (1) (2) where x = Observed value to be scaled Xmin = Minimum value of x Xmax = Maximum value of

x µ = Mean value of x σ= Standard deviation Cmin and Cmax = Network's practical limits (depend upon the activation function). The suggested neural network model is supposed to utilize a simple field test, namely the SPT (Standard Penetration Test) to predict the lateral load capacity of piles. This makes the model attractive to practitioners as well as researchers. The input parameters required by the neural network model are basically the SPT-values with depth, Pile length, cross-sectional area, circumference and the amount of steel reinforcement. RESULTS AND DISCUSSION Axial Pile Capacity During the training phase, the measured axial pile capacities are compared with the capacities obtained by BPNN and the GRNN. After the training phase, the neural network models are capable of reproducing the target output values with minimal error. Next, the reliability of the trained model in producing correct responses for a new set of data is examined. Once the training, testing and validation phases are successfully accomplished, the neural network obtained can be used as a practical design tool for driven piles. Laterally Loaded Piles Neural Network models (BPNN and GRNN) are used to predict the deflection of the drilled shafts based on the SPT-N values and the shaft geometry. The deviations from the measured deflections, in the case of

BPNN, are founded for the top lateral deflection at different levels of lateral loading. The predictions of deflection with depth at a specific load level can show deviations. The GRNN prediction gives a good approximation for the deflection. The deflection with depth correlates very well with the predicted. CONCLUDING REMARKS AND RECOMMENDATIONS The effectiveness of the analysis methods to describe the response of the soil-structure system depends to a large degree on the ability to specify the relevant material characteristics. Soil properties vary widely at a given site and the limitations of current sampling and testing techniques aggravate this variation. • Neural Network approach is one alternative that can encapsulate the variability in soil properties and interactions. Neural network paradigms were introduced for the design of piles subjected to axial and lateral loads. The real behavior of the piles is determined from comprehensive lateral and axial load tests in different projects. These data were used for the optimal design of the neural network models. The artificial neural network based design approach consists of feedforward Backpropagation Neural Network, and Generalized Regression Neural Network. According to the simulation results, the neural network approach is feasible and has been found to be more accurate than the commonly used techniques for the design of pile foundations. • The GRNN model has the advantage that it is unnecessary to define the number of hidden layers or the number of neurons per layer in advance. •

Moreover, the GRNN provides an adequate approximation of the full-scale pile test results.

Based on the results from this study, it appears that the proposed neural network models furnish a pragmatic and a reliable alternative for the current analysis and design techniques of axial pile capacity and laterally loaded piles.

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