**Developing a Bridge Condition Rating Model Based on Limited Number of Data Sets Limited Number of Data Sets**

**Developing a Bridge Condition Rating Model Based on** 

DOI: 10.5772/intechopen.71556

Khairullah Yusuf and Roszilah Hamid Khairullah Yusuf and Roszilah Hamid Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71556

#### **Abstract**

[9] Bluescope Steel. HA350 steel Datasheet Datasheets. 2017. See http://steelproducts.blue-

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[11] Standards Australia. AS5100.2:2017 Bridge Design, Part 2: Design Loads. Sydney,

[12] Standards Australia. AS/NZS1170.2:2011 Structural Design Actions: Wind Actions.

[13] Byer O, Lazebnik F, Smeltzer DL. Methods for Euclidean Geometry. U.S.A: MAA; 2010 [14] Kunkel P. Hanging With Galileo. Whistler Alley Mathematics [Online]. 2006. Available at: http://whistleralley.com/hanging/hanging.htm. [Accessed: 27 March 2016]

[15] Prince Engineering. Carbon Fiber used in Fiber Reinforced Plastic (FRP). [Online]. 2013. Available at: http://www.build-on-prince.com/carbon-fiber.html#sthash.gBoq2sJ6.dpbs.

scopesteel.com.au/category/datasheets [Accessed: 29 June 2017]

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26 Bridge Engineering

[Accessed: 3 July 2017]

Australia: Standards Australia; 2017

Sydney, Australia: Standards Australia; 2011

This chapter utilizes artificial neural network (ANN) and multiple regression analysis (MRA) to model bridge condition rating based on limited number of data sets. Since data sets are very limited and there is a gap in range of rating scale, two conditions of data sets are used in this study, namely complete data sets and data set with bridge component condition rating data are missing. Five methods are then used to handle the missing bridge component condition rating data. Three commonly used methods and two new methods are explored in this study. It seems that the performance of the model using data sets after handling missing bridge component data to fill the gaps in the range scales of the bridge condition rating improved the performance of the model. In addition, a handling method that substitutes missing data of bridge component ratings with available bridge rating data is favorable. Based on the values of root mean square error (RMSE) and *R*<sup>2</sup> , the ANN models perform slightly better than MRA to map relationship between bridge components and bridge condition rating. This concluded that ANN is suitable to model bridge condition rating compare to MRA method.

**Keywords:** multiple regression analysis, neural network, function approximation, bridge condition rating, root mean squared error

#### **1. Introduction**

The bridge condition rating is the most important part of the bridge management system (BMS) because, historically, bridge condition rating data were found to affect approximately 60% of the BMS analysis modules [1]. For BMS requirements, bridge inspectors generally use visual inspection as the first step toward condition assessment procedure unless a structure cannot be visually assessed. In through visual inspection, bridge inspectors evaluate the condition of a bridge using their personal experience and following guidelines such as

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

those found in inspector's manuals. The visual inspection incorporates many parameters and human judgments that may produce slightly uncertain and imprecise results [2]. It would be ideal to conduct physical structural tests on each bridge component, but it would be impractical and economically prohibitive to implement them, given the large number of bridges to be inspected within a given period. As an alternative, the collective judgment of the inspectors can be used to develop unified, coherent bridge inspection procedures [3]. Thus, a mathematical method such as an artificial neural network (ANN) and multiple regression analysis (MRA) can be useful to handle this uncertainty, imprecision, and subjective judgment.

quantified in certain ways during the data-mining process. Moreover, the simple methods

Developing a Bridge Condition Rating Model Based on Limited Number of Data Sets

http://dx.doi.org/10.5772/intechopen.71556

29

The performance of the mathematical model of bridge condition rating is also dependent on the quantity and the quality of data set used in constructing relationship between bridge component and whole bridge condition rating. Thus, the purpose of this study is to develop bridge condition rating model based on limited available data and different rates of missing bridge component condition rating data. MRA and ANN are utilized to map relationship between bridge component ratings and whole bridge condition rating. Four conditions of data sets are used: complete data sets (M0), data sets with one component missing (M1), data sets with one or two components missing (M2), and data sets with one, two, or three components missing (M3). Five methods are then used to handle the missing bridge component condition rating data. This study explores three commonly used methods and two new ones. The best method is then applied to substitute the missing data of bridge component condition ratings so that the bridge condition rating model can be developed from various conditions of data sets. Furthermore, the handling of the missing data also increases the size of data sets

mentioned earlier are often not suitable for improvement of the quality of the data.

and provides a more complete range for the bridge condition rating distribution.

Condition rating data have the potential to provide tremendous value to the bridge management. The condition rating data can be used to help prioritize maintenance work and decide on allocation of available budgets based on engineering and financial considerations [7]. Hence, the appropriate procedure is needed in bridge condition ratings data gathering for

ANNs are widely used as an attractive alternative to handle complex and non-linear systems that are difficult to model using conventional modeling techniques such as MRA. ANNs have been widely applied in engineering, science, medicine, economics, and environmental applications. The most common applications are function approximation, pattern classification, clustering, and forecasting [1, 8–10]. Various forms of ANNs (i.e., feed-forward neural networks: FENN, recurrent networks, radial basis functions, wavelet neural networks, Hopfield networks, etc.) have been applied in various disciplines. However, in the context of function approximations, such as bridge condition rating, the FFNN is generally chosen as the network

Chen [10] categorized and evaluated a beam bridge condition into four main bridge components, namely, substructure, bearing, beam, and accessory structure. These four components are evaluated based on 20 assessment criteria that can be inspected by close visual inspections according to Chinese Bridge Maintain Codes. Five neural network models are then developed to model substructure, bearing, beam, accessory structure, and whole bridge status. The input parameters for substructure, bearing, beam, accessory structure, and whole bridge status are 7, 2, 6, 5 and 4, respectively. He concluded that the proposed approach improves the efficiency

architecture [9] and back propagation (BP) as the learning algorithm [10–12].

**2. Previous works**

of bridge state assessment.

managing bridges under constrained resources.

The limited inspection reports maintained by the Public Works Department (PWD) of Malaysia are used as the initial data, which contain valuable information about the condition ratings of the bridge components and whole bridges. The condition rating is a numerical system, where a number from one to five is assigned to each component of the structure based upon observed material defects and the resulting effect on the ability of the component to perform its function in the structural system, as described in Ref. [4]. **Table 1** shows the condition rating system used by PWD Malaysia. The bridge components that are inspected and rated contribute to the overall bridge rating, as shown in **Table 1**. The bridge components involved are the beam/girder, deck slab, pier, abutment, bearing, drainpipe, parapet surfacing, expansion joint, and slope protection.

The original data sets are very limited and many shortcomings exist in the records such as unavailable or missing bridge component condition rating data, the whole bridge condition rating is not distributed in complete range of rating scale and many outlier data sets are exist. The outlier data are where the whole bridge rating value is larger than the maximum component rating data. The missing data problem requires a method to improve the accuracy and efficiency of the modeling of the condition rating of a bridge that utilizes a mathematical model such as MRA and ANN. In terms of BMSs, inappropriate treatment of missing data affects the performance of the bridge condition rating model and the bridge deterioration predictive model.

The common methods used by previous researchers to deal with the missing data include either deleting the missing features or replacing the missing data with zero or with the mean data of the training set [5, 6]. However, as there is a certain level of uncertainty associated with a particular case, such as the bridge condition rating data, the above method must be


**Table 1.** The condition rating system based on severity of defect.

quantified in certain ways during the data-mining process. Moreover, the simple methods mentioned earlier are often not suitable for improvement of the quality of the data.

The performance of the mathematical model of bridge condition rating is also dependent on the quantity and the quality of data set used in constructing relationship between bridge component and whole bridge condition rating. Thus, the purpose of this study is to develop bridge condition rating model based on limited available data and different rates of missing bridge component condition rating data. MRA and ANN are utilized to map relationship between bridge component ratings and whole bridge condition rating. Four conditions of data sets are used: complete data sets (M0), data sets with one component missing (M1), data sets with one or two components missing (M2), and data sets with one, two, or three components missing (M3). Five methods are then used to handle the missing bridge component condition rating data. This study explores three commonly used methods and two new ones. The best method is then applied to substitute the missing data of bridge component condition ratings so that the bridge condition rating model can be developed from various conditions of data sets. Furthermore, the handling of the missing data also increases the size of data sets and provides a more complete range for the bridge condition rating distribution.
