Keywords: structural analysis, segmentation, data errors, error models, determinants, computer algorithm.

Structures play an important role in several areas of industrial importance. The off-shore structures used in the off-shore mining of oil and gas represent an important class of complex tubular structures characterized by a large number of tubular members and of nodes where the tubes form junctions. A typical shallow water off-shore structure consists of 385 tubes and 202 nodes in a ocean depth of about 100 meters and deep sea structures will be much larger.

We had a mathematical modelling and software development project [1] funded by the Oil and Natural Gas Corporation (ONGC) of India. This project, on cathodic protection of off-shore structures [2], involved 3-D geometric modelling and also visualization of the several planar segments present in the off-shore structure. Though this segmentation process can be carried out by mere inspection for small and simple structures, segmentation of huge and complex structures by human inspection requires a physical model and involves pains-taking manual classification of the tubes and nodes.

In this paper we present a powerful computational method to perform the segmentation without manual work and physical models. However, this method, based on a fourth-order determinant, was found to be very sensitive to even small numerical errors present in the input structural data. Hence a novel error model was developed which render this algorithm error-tolerant. Two error control parameters, viz., the segment factor and the tube factor, were used.

The error-tolerant algorithm was tested against three toy structures. Errors were artificially introduced in the node data of the toy structures, while errors are present naturally in real off-shore structures. After testing the algorithm on the toy structures, we applied it to a real off-shore structure. This structure has 202 nodes, 385 tubes and is nearly 100 meters tall. To aid the development of the computer algorithm and to test it on at least one real off-shore structure, we built a physical scale model for this structure (of nearly 1 meter height) and, by an elaborate manual inspection, classified the nodes and tubes present in this structure into a total number of 16 planar segments. We ran our algorithm on this structure for several settings of the segment factor and the tube factor. The results showed perfect agreement with the results of the actual manual inspection performed on the physical scale model even in the presence of errors in the structure data. Our experience with the present segmentation routine shows that, within four or five simulation runs, the error control parameters can be optimised for a proper classification of the segments and tubes in real off-shore structures.

We have delivered to ONGC a module based on the present segmentation algorithm, as a part of a comprehensive software for cathodic protection of off- shore structures using the Boundary Element Method. ONGC owns more than hundred off-shore structures in the Bombay Off-shore Region. The Segmentizer module helps in the segmentation of these complex structures without a need to build physical scale models of these complex structures for cumbersome manual inspection. The module based on our error-tolerant segmentation algorithm has already been applied successfully on several of these off-shore structures by ONGC. We also believe that the present method may find use in artificial intelligence as applied to structural engineering problems.

1

Mathematical Modelling and A Comprehensive Software Package Based on the Boundary Element Method for Cathodic Protection in Off-shore Platforms, Project funded by the Oil and Natural Gas Corporation of India, July 1995 - April 1998.

2

V.S. Ramanan, M. Muthukumar, S. Gnanasekaran, M.J. Venkataramana Reddy, B. Emmanuel, "Green's functions for the Laplace equation in a 3-layer medium, boundary element integrals and their application to cathodic protection", Engineering Analysis with Boundary Elements, 23, 777-786, 1999. doi:10.1016/S0955-7997(99)00025-9

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