Solution
Figure 1 shows a flow chart of rail track risk assessment. The risk of the system can be calculated by a combination of the likelihood of failure (LOF) and the consequence of failure (COF).
In this case, the LOF is calculated by the likelihood of defective tracks. Historical data, including failure types and value of damage factors, is essential to establishing the RBI model. In order to obtain the consequence of failure, some additional parameters such as cost of maintenance and route information are required as well. The RBI model provides a risk matrix to inform inspection or maintenance regimes.
The techniques that are shown in Figure 1 are described below:
1. Likelihood of defective tracks by Gaussian process regression
Based on a review, a nonparametric kernel-based probabilistic model, namely Gaussian process regression (GPR), is applied due to its advantages of easy automation, accuracy, and less stringent data requirement. In this technique, the training data is composed of four predictors and one response variable. The predictors include average annual traffic density, average population density, average maximum speed allowed on the tracks and season. Rail age and traffic load data should be included if available. The response variable is the likelihood of defective tracks. A Hold-one-out validation method is applied to verify the mode, and repeated several times until each row has been used for the validation set. The true and predicted failure data are presented in Figure
2. Consequence of broken rails
The COF is another necessary input for risk assessment models. In this case, three categories of costs associated with rail defect inspection and the corresponding maintenance actions are considered – dealing with:
- a very seriously broken rail that causes derailment
- a broken rail that does not cause derailment;
- a small rail defect that does not grow to a broken rail
3. Risk assessment model
The risk assessment function can be written as: Ri = Pi X Ci
where
Pi = the likelihood of defective tracks, unit: defect/mile (or yards);
Ci = the cost consequence of failure for rail tracks, unit: pounds/defect;
Ri = the risk caused by defective tracks, unit: pounds/mile.
The risk matrix for rail track inspection is presented in Figure 3.
Different risk represents different suggested inspection time and interval. The specific suggestions need expert inputs to the model.
The model is able to develop a risk profile for each line and each segment, see Figure 4.
Based on the risk assessment, the model can also assess the remaining useful life and optimise inspection using machine learning methods, i.e., Gaussian process regression, support vector regression, in real time if condition monitoring data and commissioning time data are available, see Figure 5.