**2. Previous works**

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.

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

**Rating scale**

28 Bridge Engineering

**General definition**

1 No damage found and no maintenance required as a result of inspection

provision of a load limitation traffic sign, or replacement work

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

2 Damage detected, and it is necessary to record the condition for observation purposes

inspection to determine whether any rehabilitation works are required or not

3 Damage detected is slightly critical, and thus it is necessary to implement routine maintenance work 4 Damage detected is critical, and thus it is necessary to implement repair work or to carry out detailed

5 Being heavily and critically damaged, and possibly affecting the safety or traffic, it is necessary to

implement emergency temporary repair work immediately, rehabilitation work without delay after the

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 managing bridges under constrained resources.

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

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 of bridge state assessment.

Li et al. [13] utilized ANN to evaluate a bridge conditions based on substructure, superstructure, deck, and channel conditions. In their proposed model, the training cases converged very well, but for the test cases, the prediction from the network is consistent with the target in about 60%. They concluded that the low prediction accuracy affected by the data used in training the network is not sufficient for the network to generate proper weights to precisely model the input– output relationship. Another reason was inconsistency in the evaluation results due to subjective factors observed in the inspection data, which are used to train and test the neural network.

Since the availability of data sets with complete condition data of bridge component were very limited, utilizing incomplete sets by handling missing value with the appropriate treatment is expected to improve the performance of the model. Furthermore, upon observation of the available data sets, it was found that there is a big gap in the bridge condition rating distribution, where there were no complete data sets available for a bridge condition with a rating of 4 and only four pairs of complete sets of bridge conditions with a rating of 5 available. Consequently, finding the best method to handle this problem is an important step prior

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

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

31

The original data sets include 1244 data sets from the last 4 years of inspection records of 311 single-span concrete bridges. Among these data sets, only 579 sets have complete rating data for components and the whole bridge condition. From these 579 data sets, a large number of the bridge condition rating data sets have repeated data. When constructing the model of bridge condition ratings through an ANN and MRA, they provide nothing new as the information is redundant. To avoid this redundancy, only one of the data sets with the same data is retained and the others are deleted. Furthermore, these available data sets are also adjusted to remove the outlier data sets where the bridge condition rating value cannot be larger than the maximum component rating data. After deleting the redundant and outlier data sets, there are 157 data sets left with almost all of them having a rating of 1, 2, or 3. However, bridges with a condition rating of 4 do not have complete component rating data, and only three pairs

As explained in the previous section, all data sets for bridges with a rating of 4 are incomplete. In this study, the data sets that have 1–3 components with missing value are considered and handled with different methods to provide more data and fill the gap in the bridge rating scale distribution. The number of data sets for M0, M1, M2, and M3 are 157, 226, 252, and 267, respectively.

to constructing the model of the bridge condition ratings.

with a rating of 5 are available, as shown in **Figure 1**.

**Figure 1.** Bridge rating distribution of completed data sets (M0).

**3.1. Data preparation**

In most countries, there exists a large time gap between the dates of the construction of the bridge and the adoption and implementation of the relevant BMS [14]. There is a general leaking in such BMSs' database such as inconsistency of data sets and much bridge component condition rating is unrecorded. Another example of how bridge condition rating data can go missing is the difficulty in obtaining information and expensive testing of some bridge components. The missing data constitute the largest fraction of the difficulties in analyzing the data, making constructing predictive ratings, and other decision-making processes that depend on these data. Furthermore, it is impossible to build a convictive classification model with missing data because the missing data affect the integrity of the dataset [6]. Zhimin et al. [6] used five methods to handle missing data in their classification problem. The methods are as follows: deleting missing data, replacing missing data with zero, replacing missing data with the mean value of all the data of the training set, replacing missing data with the mean value from the same label data of the training set and predicting the missing value using a feed-forward backpropagation ANN. Markey et al. [5] compared three methods for estimating missing data in the evaluation of ANN models for their approximation problems. These methods are as follows: simply replacing the missing data with zero or the mean value from the training set or using a multiple imputation procedure to handle the missing value.
