Model Assumptions

The model assumptions are mapped to the relational database to configure the relationships between classes and later used to define the expression of the variable in the model library. The model assumptions contribute to the modelling specifications, which are fixed for a specific problem but varies for different problems. They can be defined by industry standards, guidelines, the nature of the system itself, the practical experience made by domain experts, feedback from the previous models or aided by some machine learning techniques. This subsection describes the key aspects of the assumptions considered here, but detail functions can refer to Chapter 4:

• The number of deterioration states: Each asset is usually rated with a state repre- senting its level of functionality. For example, a 3-point grading system shown in Section 6.1.1 for GB bridge and 10-point grading system shown in Section 6.1.2 for US bridges are used. Grading systems are normally adopted from industry standards and are often used to identify the associated risk of the asset. They vary from infrastructure type, countries, and sometimes, inspection agencies. An n states grading system results in n − 1 transitions represented in the instantiation of class Transition. For inference benefits, they are aggregated using the binary factorisation when evaluating the state of a component as discussed in Section 4.3.1.

• The choice of transition distribution: Different distributions can be used to estimate transition times of deterioration, based on their goodness of fit. The goodness of fit of the distribution is usually done by visual observation and hypothesis tests [115]. A range of study has been developed to find the best fit distribution of asset state deterioration times. For example, the exponential distribution has been used for railway

track [63, 67] and the Weibull distribution for bridges [3, 94] (see Section 2.3.1). The choice of distribution defines the function of the variable transition distribution and variable deterioration time. The number of parameters in the distribution’s pdf fixes the number of instances of the Parameter class for each Transition (e.g. exponential distribution with one parameter and Weibull distribution with two parameters).

• The classification of assets: Under the assumption that similar assets may deteriorate similarly, we could use their features to quantify assets into different groups - where each group is assumed to have the same deterioration rates as shown in Chapter 5. By doing so, historical data can be pooled and used to learn assets deterioration parameters between groups.

– Grouping by features: The levels of asset’s features define the asset group. However, first, we need to consider how many features, what features to be used to decide the grouping and their weights. This information configures the structure of class Group and class Feature. It can be done by experts knowledge, where they believe there are dominant features that are significantly affecting the deterioration of assets. For example, masonry bridge is considered to decay significantly slower than other bridge types from personal communication with a bridge engineer. By having this information, we can consider grouping bridges by their materials. Experts can assign the weights of features, but if this information is unavailable, uninformative priors can be assigned. The grouping can be refined by feedback from the previous models.

– Individual feature levels: We can use a scalar like low, medium and high influence on deterioration rate as shown in Section 5.3.2 to quantify the level of features. Either experts or clustering techniques can do the assignment of feature level. For example, for feature material, experts can assign bridges built with masonry has a low influence on accelerating its deterioration rate, while bridges built with metal has a high influence. Clustering technique can be used to divide assets with different feature values into different clusters using the training data. Each cluster can be modelled with a feature level. Multiple features, where each feature has its feature level and weight, are later aggregated using a weighted mean function with a variance about the confidence level about their weights.

– Prior knowledge about deterioration characteristics: Once the groups are defined, we can ask experts to assign the priors for the group parameters (see Section 4.1.3 about how to elicit priors of parameters in a Weibull distribution). This information is mapped to class Parameter accompanied by variances in class Local

Parameter about the differences between group parameters and local parameters. In the case where experts choose not to group assets, the prior of the parameter becomes the prior of the asset’s parameter itself.

• The asset’s components and their configurations: Asset could be considered as a single component system or a multi-component system depending on its nature. These components can be assembled with various configurations such as in parallel, series or bridge structure as discussed in Section 2.3.3. For traditional parallel or series configuration, we can define the aggregation from class Component to class Asset as a maximum or minimum function as an FT gate. For bridge structure, we can define a weighted mean function where each component is given a weight by experts representing its importance in deciding the condition of the asset. Similarly, this can also be extended to describe a parallel or series system with weights using functions like weighted maximum and weighted minimum.

• The available repair actions for components and their effectiveness: Different components may have different repair actions, and different actions may have different effectiveness in restoring their states. Examples can be found in Section 6.3. The configuration of its CPT can be learned from historical records, such as the frequency of restoring the component to a particular state using a specific repair action or given by experts.