Risk Calculations

This chapter describes how risk in the pipe network is calculated through a combination of probability of failure and consequence of failure. Probability of failure is estimated using data-driven methods that take into account both historical events, pipe properties, and network structure, while consequence is calculated based on the effects a failure will have on supply, operations, and affected areas. Together, this provides a more comprehensive and decision-supporting risk picture that can be used for targeted prioritisation of measures.

Probability of Failure

Probability of failure is calculated using machine learning trained on historical failure and maintenance data from many Norwegian municipalities.

The model uses, among other things, age, material, and other properties of the pipe network, combined with recorded incidents and work orders. In addition, the algorithm takes into account the network structure — i.e. how pipes and nodes are connected in the system. This is done using a graph-based machine learning model (GNN) that analyses connections and patterns in the network.

The result is a probability value indicating how likely it is that a component already has, or will soon develop, a failure.

Based on data from:

Pipe database:
- Pipe function (water, wastewater, stormwater, with subcategories)
- Material type
- Installation year
- Geographic position in the pipe network
Logbook entries / operational data:
- Break history for pipes of similar types
- Blockage history for pipes of similar types
- Pipe inspection data

Unique to PipeFusion is its ability to account for properties not directly derived from the source system. Through the graph data model, properties such as travel distance to other known failures through the network, connection density, neighbour density, and the proportion of network and connections up- and downstream of the pipe being assessed are recognised. This is used to strengthen results independently, but also makes it possible to assign a value when installation year or material is unknown — so you never end up with missing results for individual pipes.

The calculated probability from PipeFusion is accurate for around 90% of pipes. However, if users do not know which pipes the model is unexpectedly inaccurate for, they will always be sceptical of the result. This can be resolved by displaying a reference calculation based on historical statistics in parallel — typically Norsk Vann's table for prioritising pipe replacement. This makes it easy to see where there are large deviations between PipeFusion and the expected result.

The calculated probability of failure in PipeFusion provides a more nuanced and precise picture because it combines machine learning, historical failures, network structure, and local conditions — not just age and material. In contrast to Norsk Vann's statistics, which are broad and often produce large categories with high maintenance needs, PipeFusion can better distinguish between high and low risk within the same age and material group. This makes it possible to prioritise measures more accurately and deploy resources where the risk is actually greatest.

PipeFusion is also a much more user-friendly and dynamic way to present results, and easier to keep updated without manual processes.

Consequence Calculations

Consequence is calculated by analysing what happens in the network if a specific element fails or stops functioning. The model is based on methods from mathematical graph theory, and therefore requires the network to be stored as a graph database to run — meaning it is calculated on the output from PipeFusion, not raw data. The fundamental principle is to calculate what proportion of the network loses connectivity if a pipe is removed, and the method works systematically through the network.

Wastewater

The wastewater network is defined with a flow direction, so the method starts at the outermost point of the network — a terminal node — and follows the flow direction while counting backwards how many elements depend on the given pipe. The result is normalised based on position and hierarchy and given a value between 0 and 1. In addition, categories 1–5 are produced so that results can be compared with other approaches or set up as a risk matrix in accordance with the DiVa method.

Water

Water supply is somewhat more complex, as there is no fixed flow direction and pipes may belong to a ring system. First, all routes water can travel from treatment plant to terminal node are calculated, and pipe connections belonging to many routes receive higher consequence than connections belonging to only a few possible routes.

For water, redundancy is also taken into account, so that alternative supply routes can reduce the consequence. Pipes that do not belong to a ring system are categorised as a «bridge» and the consequence is calculated from how many pipes lose connectivity upon removal. Pipes that are part of a ring system are identified through graph algorithms that look for «how many connections must be cut before it becomes completely disconnected from the rest of the network». All pipes in the same group then receive the same consequence value.

To reproduce criticality, pipe diameter is used as a factor in consequence calculations within each ring system, so that the largest diameters receive the highest consequence, and smaller pipes are graded down based on their size relative to the largest pipe in their group. The result is a consequence value that expresses how serious the effect of a failure will be for the system as a whole — including both loss of water supply or poor pressure at subscribers, and local damage due to large volumes of water in the wrong place.

Risk Calculations