Keywords: quantity estimate, cost estimation, conceptual design, highway bridges, neural network, bidding process.

Observations of bridge bidding practices have shown that the area of cost estimation apparently relies on three types of quantity estimate offering three different levels of accuracy. At the lower level, where the overall cost of a bridge is required, the cost per meter square is estimated based on the past experience of senior bridge designers and multiplied by the total bridge area. At the upper level, where an accurate estimate is required, almost a complete bridge design is performed and relevant quantities are taken off. Typically, this detailed estimate would involve one man-week of work to cost two design alternatives[1]. Unfortunately, the third type of estimate, which has an in-between level of accuracy, is not well established. This type of estimate is called preliminary quantity estimate and it aims to provide bridge designers with the approximate quantity of main bridge components in an economic and timely fashion. It also facilitates comparing different alternatives of bridge design for bidding purposes.

The work with developing computer models that support the preliminary quantity estimate and conceptual design of highway bridges has been realized by many researchers since early 90's. Most of these models are knowledge-based systems (KBS) that make use of heuristics elicited from expert bridge designers to give quick and reliable estimates. More information about these systems can be found in references[1,2,3]. Although these systems are working successfully, they have some restrictions in their performance and expandability[4]. These do not give incorrect answers but they fail to give any answer at many times. This usually occurs when there is no knowledge to handle the given situation. KBS's also cover only a portion of the problem domain, and their ability to be automatically updated when new cases are encountered is poor. In addition to these problems, the knowledge acquisition from bridge experts is the most critical process in developing a KBS since the acquisition rate is unacceptably low and the interpretation of the resulting knowledge varies among bridge designers[5]. Another category of models that support preliminary quantity estimate is the mathematical models. The development of these models is not a simple task because the statistical or mathematical formula that best fits the available data cannot be easily determined and the interaction among the independent variables cannot be accurately considered.

Because of the restrictions of KBS's and the inconvenience of mathematical models, research interests during the last decade have been shifted to benefit from machine-learning techniques established in the Artificial Intelligence (AI), such as: Artificial Neural Networks (ANN's) and Case-Based Reasoning (CBR). An ANN is an information-processing system that has a brain-like structure and certain performance characteristics similar to biological neural networks[6]. ANN's solve problems based on learning from a set of examples that have been encountered and without bearing the developer the burden of designing the underlying algorithm.

In this paper, an ANN model with back-propagation learning algorithm were employed to transfer the knowledge encapsulated in the design of 22 overhead prestressed concrete (P.C.) bridges constructed in Egypt, into usable knowledge. This model was developed to estimate the concrete volume and prestressing weight in the superstructure of bridge navigable spans. These items were selected because their cost represents 40% of the cost of these spans. Estimating the quantity of remaining items follows the same procedures and can be done in future research. The input attributes used in this model were: main span length, superstructure type, structure system, construction method, contract type, and design type. The BrainMaker simulator was used in training and testing the model because of its simplicity and affordability. For optimum network configuration, parametric studies were carried out and their results can be summarized as follows: Learning rate = 0.6, number of hidden layers = 2, and number of neurons per hidden layer = 20. Testing the developed network was carried out using cross-validation experiments. Testing results showed that the network error was 7.5% in estimating the concrete volume and 11.5% in estimating the prestressing weight. These results indicate that ANN's have great potential to be decision support tools for preliminary quantity estimates.

1

Moore, C. J., "Computational Decision Support for Preliminary Bridge Costing", International Association for Bridge and Structural Engineering IABSE, 1995.

2

Miles, J. C., "Integrated Innovative Computer System for Conceptual Bridge Design", International Association for Bridge and Structural Engineering IABSE, 1995.

3

Cauvin, A., and Stagnitto, G., "General Purpose Expert System for Preliminary Structural Design", International Association for Bridge and Structural Engineering IABSE, 1995.

4

Roddis, W. M. K., and Bocox, J., "Case-Based Approach for Steel Bridge Fabrication Errors", Journal of Computing in Civil Engineering, ASCE, Vol.11, No. 2, 84-91, 1997. doi:10.1061/(ASCE)0887-3801(1997)11:2(84)

5

Yeh, Y., Kuo, Y., and Hsu, D., "Building KBES For Diagnosing PC Pile With Artificial Neural Network", Journal of Computing in Civil Engineering, ASCE, Vol. 7, No. 1, 71-93, 1993. doi:10.1061/(ASCE)0887-3801(1993)7:1(71)

6

Fausett, L., "Fundamentals of Neural Networks: Architectures and Applications", Prentice Hall, 1994.

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