Maintainers often record their estimation of the asset’s condition during each inspection, and an asset management database often contains information about the asset’s features. If these inspection records and feature information are available, we can use them to infer the rate of an asset’s deterioration. This section introduces inference from these inspection records and explains how to select factors that may an impact on the deterioration rate.
2.2.1
Deterioration Time Data
The majority of bridge inspection records are collected from traditional on-site inspections. These on-site inspections are often performed periodically. Generally, inferring a deteriora- tion rate requires sufficient data derived from historical asset condition information made from inspection or maintenance [94].
The deterioration time (also called sojourn time or occupation time in some studies) of each state can be inferred from condition data and their corresponding inspection time. Since most bridges are inspected periodically, the inspection data may not reveal the actual time the structure transitioned from one condition to another: suppose, for example, that the most recent inspection shows a structure is in state 8 but was in state 9 at the previous inspection. This situation does not imply the deterioration time from state 9 to 8 is the time gap between these two inspections: the deterioration may happen anytime between these two inspections. This limitation in the information available is referred to as ‘censorship’, introducing uncertainty to the observed deterioration [101]. We know only that the structure deteriorated before an inspection (left censored), between two consecutive inspections (interval censored), or after the most recent inspection (right censored), rather than a specific time point.
Apart from the uncertainty in the actual time of condition changes, for some states, the number of inspection records is often small. Periodic inspection policy and slow deterioration process are two main reasons. Since an on-site inspection is conducted only every year or every few years, this activity usually only provides us with a limited number of records. For example, as described in Section 2.1.4, in GB, rail bridge visual inspection is every one year and detail inspection is every six years; while in the US, bridge inspection is performed every two years. These long inspection intervals can only infer a limited amount of deterioration data. Besides, since many infrastructure assets, such as bridges, decay slowly, transitions from one state to another do not occur often. For example, in the 26 years of inspections recorded in the NBI database, some bridges have not even deteriorated once. Finally, most of the bridges are in good or fair conditions (at state 5 or over) because maintainers often
perform interventions to prevent further deterioration when assets are in poor condition. As of 2017, only 7.7% of the bridges are at state 4 or less that could produce deterioration data for lower states.
2.2.2
Features Influencing Deterioration
As discussed in Section 2.1.3, there are many features of an asset or its use that can influence its deterioration rate. It is possible to give a more accurate prediction of the condition of an individual asset by considering the specific values of the features that impact the rate of deterioration [177].
Individual structures with same features may share the same deterioration characteristics, deteriorating at a similar rate. We can use this assumption to separate the overall population into different groups, so that the deterioration rate is estimated within each group. However, each structure is often associated with many features. For example, each bridge has over a hundred features recorded in the NBI database. Considering too many features can be a disadvantage as it takes too many resources and results in slow computations. More importantly, after reaching an optimal number of features, increasing the number of features further causes a decrease in accuracy [80], for example, by overfitting. Therefore, to provide individualised deterioration predictions, one of the challenges is to reduce the feature dimension into a small subset. With a few predictive features, we can separate structures into groups so that, within each group, structures are assumed to deteriorate similarly.
A framework to give individualised deterioration predictions in this way was developed in Chang [23]. It first reduced the feature dimension of the dataset to select a small subset of features as important features, and then grouped assets with the same feature values. Each group was modelled using a Markov model to model multi-state deterioration, the transition probabilities of the Markov model were learned using logistic regression. Individualised deterioration prediction was then performed based on the group the asset belongs to. In Chapter 5, we compare this approach with our methods.
To reduce the dimension, Chang [23] first conducted a covariance analysis to remove highly correlated variables and later used a penalised regression to rank features based on their importance in deciding the deterioration time. Feature selection has been intensively studied in the feature engineering domain. Unlike feature extraction methods, such as Principal Component Analysis, that synthesise new features which may not have intuitive meaning, feature selection is more suited to the problems addressed in our work since it finds a subset of features from the candidate pool. These features are more meaningful than synthesised features, so can be interpreted by engineers.
Based on the assumption that we can remove many less relevant features without losing too much information on the response variable (e.g. the deterioration time), feature selection aims to reduce the set of features to a manageable size that is still representative enough to reflect the variability of behaviours. Plenty of techniques have been developed for feature selection, of which, filter and wrapper methods are the two most developed areas.
Filter method applies a statistical measurement to evaluate the feature space. Because of its computational efficiency, it is usually used as a preprocessing technique. Chang et al. [24] measured the correlation between variables in the NBI database. Strongly correlated variables (with a correlation over 0.90 or smaller than -0.90 as suggested by Ayyub and McCuen [10]), considered to imply redundant information, were identified. Among those highly correlated variables, they only kept the features with the highest correlations with the response variable and eliminated the rest. This method can slightly reduce the feature space size while maintaining the predicting power of the features. However, we still need further dimension reduction, because, among the remaining features, many of them do not have strong correlations with the response variable.
Wrapper methods evaluate a subset of features, where different combinations are gener- ated, evaluated and compared with other combinations. A learning model is used to estimate a subset of features and assign a grade to each combination based on a given model metric. Various studies have been proposed to study the feature importance [181], of which, random forest is one of the most popular methods. Unlike penalised regression applied in Chang [23], random forest does not assume a linear relationship between the features and the response variable (e.g. deterioration time). Random forest is an ensemble method used to performs variable importance evaluation by weighting multiple decision trees independently developed from bagged training samples.
In the random forest, each node in the decision trees is a value of a single feature that is designed to split its descendent nodes, so eventually similar response variables end up in the same pool. Two importance measurement functions of the features proposed by Breiman [20] are commonly used in the random forest: Mean Decrease Impurity (MDI) and Mean Decrease Accuracy (MDA). MDI searches to spilt which variable would give the lowest purity (for example, Gini impurity) given the response variable. Within a tree, each feature is evaluated by how much changing the value of the feature would decrease the weighted impurity of the tree. The impurity decrease from each feature are thus averaged in the forest, and the features are ranked accordingly: the lower the decrease in the impurity the better. MDA measures the loss of accuracy. By randomly permuting the value of a single feature that matches the distribution of the samples, this algorithm computes the accuracy of the tree given the response variable. By repeating this process for each feature, the mean loss
of accuracy of each feature in the whole forest is obtained and used to rank the features accordingly.
Strobl et al. [165] made a comparison between these two measurements. It reveals that MDI measurement is biased towards features with more categories. This bias is a challenging problem for the NBI dataset because it involves mixed data types, where some are binary (e.g. whether the structure is flared) and some have more than 20 categories (e.g. feature maintenance responsibility has 29 categories). Though Strobl et al. [164] later claimed that MDA measurement is also biased as it favours features highly correlated to other variables. To avoid this, when applying the MDA measurement, we can first preprocess the feature space to remove variables that are highly correlated with any of the features.
Though Chang [23] provides us with a framework to perform individualised prediction, the challenges of uncertainty in the deterioration data and learning the deterioration rate for those asset groups with limited data amount remain untouched. Since it is possible to separate assets into different groups by their feature values, we could use what we have learned about large groups to help to learn the deterioration rate of asset groups with limited data. Later in Chapter 4 we develop a model based on this idea and validate it in Chapter 5. Section 5.3.1 gives more details about how we perform feature engineering in our case study.