Hackathon 2019 solutions – Team Green
A cost-optimal bearing inspections and replacement decision support system.
Replacement of bearings will constitute a major maintenance cost for great belt bridge. Analysing the monitoring data, an accumulated movement of up to 50 meters per year is found. The movement is causing a gradual deterioration of the PFTE sheets, and the estimated lifespan is believed to be approx. 30 years. The movement is caused by environmental factors, causing the long bridge sections to expand and contract continously. Figure 1 shows some movement data from sensors.
Inspired by Risk-Based Inspection planning, which was developed for the operations and maintenance of offshore structures during the last four decades, we developed a mathematical model for optimimal bearing inspection and replacement. The model employs Bayesian statistics and cost-benefit analysis to include inspection and monitoring data in a decision model which minimizes expected costs.
Why such a model? The information from various sensors can be valuable, but any value is only effectuated through decisions of operation and maintenance. Without such a model, we cannot know whether a sensor is valuable or just an extra cost for the operator.
We begin with a deterioration model. We assume that the bearing wears out with a constant deterioration rate. Figure 2 illustrates the basic problem.
Next, we need to determine the causes of the deterioration. A rigorous analysis of these is not easily made, but with a Bayesian net, which is a simple way of modelling causality, engineering judgement can be used to establish an estimate. It could look like this (figure 3).
Each of the gray nodes represent something that can be measured using sensors or inspections. When a measurement becomes available, the model in figure 2 is updated to give an improved estimate of the sheet thickness and rate of deterioration.
For the example, we simplify the problem to the 3 nodes inside the dotted box. To model the time-varying deterioration, the nodes are repeated for each inspection event, e.g. once every year. (figure 4).
The costs associated with actions must be provided by the operator. For this example, we’ve assumed the cost of reactive replacement to be 50 times the cost of preventive replacement. Now we are ready to calculate. Using the open source Bayes Net Toolbox, the optimal decisions based on measurements are output, and the expected costs are calculated up-front. In this example the expected cost are
- for only making reactive replacements = 100
- without inspections, but optimally planning replacement = 8
- using inspections = 2
The reduction from 100 to 8 shows how valuable bridge maintenance is. The reduction from 8 to 2 is called the Value of Information. This tells us the benefit of inspections, and can be used to optimize inspection intervals.
At this level of detail, the concept may appear overly complicated and not constitute a real improvement over a simple trendline in a spreadsheet. However, the real benefit comes with the inclusion of monitoring data. The model ensures that any information used will have value. Furthermore, the net is easily expanded to include multiple bearings, complicated cost functions, etc.
See the ppt presentation here.
Read more about the other proposals here:
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