# Back Analysis Based On Som-Rst System

## H. Owladeghaffari

Department of mining & metallurgical engineering, Amirkabir university of technology, Tehran, Iran 

## H. Aghababaei

Faculty of mining engineering, Sahand university of technology, Tabriz, Iran ABSTRACT: This paper describes application of information granulation theory, on the back analysis of "Jeffrey mine- southeast wall-Quebec". In this manner, using a combining of Self Organizing Map (SOM) and rough set theory (RST), crisp and rough granules are obtained. Balancing of crisp granules and sub rough granules is rendered in close-open iteration. Combining of hard and soft computing, namely finite difference method (FDM) and computational intelligence and taking in to account missing information are two main benefits of the proposed method. As a practical example, reverse analysis on the failure of the southeast wallJeffrey mine - is accomplished. 

## 1 Introduction

Back analysis is a reverse procedure, which is to solve the external load or partial material parameters, based on the known deformation and stresses at limited points and the partially known material parameters (Zhu&Zhao, 2004). 

In most geotechnical engineering problems, it is often necessary to know the in situ field, material mechanical parameters, and even the mechanical model, by utilizing the monitored physical information such as deformation, strain, stress, and pressure during construction. The back analysis method, based on the required input physical deformation, can be divided in to deformation back analysis method, stress back analysis method and coupled back analysis method (Sakurai et al, 2003). The complex feature of rock mass, associated structures and the difficulty of interpretation of the interaction of excavation and rock mass are the main reasons to deploying of back analysis methods in rock engineering. 

Generally, two main procedures of back analysis methods have been pointed in the literature: inverse and direct approach (Cividini et al, 1989). In reverse method, the mathematical formalization is inverse of ordinary analysis. In this process, the number of monitored data is more than the unknown parameters, so that by utilizing of optimization techniques, the unknown parameters are obtained. The main advantage of such method is an independent spirit in regard of the iteration operations, which causes to reducing of calculation time, sensibly. Direct approach, is a process associated with the cycling optimization (aim is to minimize the fitness function). 

Application of direct approach, to evaluation of problem based non-linearity and employing of heuristic optimization methods such Ant Colony (ACO), 
Particle Swarm (PSO), and Simulated Annealing (SA) are two main results. So, back analysis based on interactions of hard computing and soft computing methods can be settled in direct approach. As an initial over view, 1-1 mapping methods can be supposed as hard computing such analytical, numerical or hybrid methods, whereas soft computing methods (SC), as main part of not 1-1 mapping methods, is a coalition of methodologies which are tolerant of imprecision, uncertainty and partial truth when such tolerance serves to achieve better performance, higher autonomy, greater tractability, lower solution cost. The principles members of the coalition are fuzzy logic (FL), neuro computing (NC), 
evolutionary computing (EC), probabilistic computing (PC), chaotic computing (CC), and machine learning (Zadeh, 1994). 

Utilizing of soft computing methods besides hard computing methods, such support vector machine (Feng et al, 2004) and neural network (Pichler et al, 2003), in the reverse procedures have been experienced, successfully. Advancing of soft computing methods, under the general new approach, namely information granulation theory, has been opened new horizons on the knowledge discovery data bases. Information granules are collections of entities that are arranged due to their similarity, functional adjacency, or indiscernibility relation. The process of forming information granules is referred to as information granulation (Zadeh, 1997). There are many approaches to construction of IG, for example Self Organizing Map (SOM) network, Fuzzy c-means (FCM), rough set theory (RST). The granulation level, depend on the requirements of the project. The smaller IGs come from more detailed processing. On the other hand, because of complex innate feature of information in real world and to deal with vagueness, adopting of fuzzy and rough analysis or the combination form of them is necessary. In fact, because of being the complex innate of crisp, rough or fuzzy attributes, in the natural world, extraction of fuzzy or rough information inside the crisp granules, can give a detailed granulation. To develop back analysis based new soft computing approaches and taking in to account of a mathematical tool for the analysis of a vague description of objects, as well as rough set theory, a 