|NDT.net||January 2004, Vol. 9 No.01|
A Risk Based Approach to Determine Ultrasonic Inspection Frequencies in Railway ApplicationsJorn Vatn , Hans Svee
The Norwegian National Rail Administration
7462 Trondheim, Norway
6th Proceedings of the 22nd ESReDA Seminar, Madrid, Spain May 27-28, 2002
AbstractIn railway applications the rails are regulary inspected by means of ultrasonic techniques to detect cracks before these develop to rail breakage's. Usually the measurement equipment is mounted on a vehicle operating at a speed of 40-50 km per hour. The current inspection intervals in Norway are based on experience from other countries, international recommendation etc, but currently these intervals have not been evaluated based on cost benefit analysis. The yearly cost of inspecting the Norwegian network comprises several hundred thousands of Euro. On the other hand there are significant costs if cracks are overlooked leading to rail breakage and a possible derailment. In a pilot study JBV (the Norwegian National Rail Administration) has developeda probabilistic model wich has been used for optimising the intervals for one of the major line in Norway. The results show that yearly cost savings of the order of 35 000 Euro could be achieved for that line by changing inspection intervals from 24 months to 12 months. The most important factors in the model are. i) number of cracks initiated per year, ii) expectation and variation of the P-F intervals, iii) measurement precision, iv) cost of inspection, v) cost of derailment and vi) cost of replacing rails.
1.IntroductionTo ensure safe railway operation it is important that the rails are free from defects such as cracks, geometry failures etc. In modern railway operation there exist two types of monitoring cars for the rails:
2. ModelIn order to optimise the "Ultrasonic inspection" in Figure 1 it is necessary to establish a more comprehensive model. A basis for such modelling is the use of socalled influence diagrams. In the JBV study the influence diagram proved very efficient as a communication tool between the analyst, the experts and the safety department.
The arrows represent the relations ( influences) between the nodes in the diagram, i.e. cause and effects. The arrows only indicate that there is a relationship, but do not say anything about how strong this relationship is.
The diagram is a basis for setting up the mathemetical model that is used in the final optimisation.
Influence diagram for ultrasonic inspection
The starting point of the diagram used in the present study is the number of rail cracks (# det. Cracks us. ) The number of rail cracks are influenced on many factors, and only the main factors are shown in the diagam: traffic load, temperature/season, and quality of the material. These factors influence the P-F interval as well.
Some cracks are deteced by USI (# det. Crack USI) some others are not (#undet. Crack USI). However, a couple of cracks that are undetected by ultrasonic measuring, can be detected in other ways ( # det. cracks by visual obs. etc. ), e.g. visual inspection. They implicate- together with the detected cracks by USI - planned rail renewals. A couple of cracks always remain undetected in the rail ( # det. undet. cracks). The others lead to rail breakage ( # rail breakages). A large portion of the rail breakage's can be detected by Centralized Train Control ( # det. breakages by CTC) and other detection methods such as visual inspection, by train personnel, etc. ( # det. breakages by visual observ. etc.). The repair of the detected breakage's results in non-planned rail renewal. The remaining rail breakages lead to derailments or other damages. Table 1 explains the content of the nodes used in the influence diagram in Figure 2.
The point "P" is the first point in time where we are able to reveal the outset of a failure. When the progression is above some value a breakage/failure will occur (point "F" ). The length from a potential failure is detectable until a failure occurs is denotes the P-F interval TPF. The legth of the P-F interval is assumed to vary from time to time because cracks can be initialized in diffrent places of the rail and the crack propagation depends on several diffrent facors etc. The length of the P-F interval should therefore be treated as a random quantity as illustrated in Figure 4.
Periodic ultrasonic inspection is conducted at intervals of length t to detect potential failures. The length of the inspection intervals should not be longer than the average P-F interval. However, since the P-F interval varies from time to time, and because there is also probability that a potential failure is not revealed during and inspection, the inspection interval should be shorter than the average P-F interval. In Appendix A a model to calculate the failure probability in this situation is presented.
3. Parameter values and cost figuresIn order to optimise the inspection intervals for ultrasonic inspection we need to assess the parameter values and cost figures used in the influence diagram. We differentiate between two types of figures:
Number of cracks and P-F interval lengths
Palese and Zarembski (2001) published that as rail accumulates tonnage, it tends to develop more internal fatigue defects, based on various factors such as metallurgy of the rail, traffic (to include such factors as axle loading and speed), track support conditions, etc.
Influence of temperature/season
Figure 5 shows the number of rail breakage's found in the railway statistic versus month number. The values for Bergensbanen, Dovrebanen and Sorlandsbanen are shown in the diagram and in addition the total summation of the breakage's on the three track sections. If we summarize the total values for winter, spring, summer, and autumn the seasonal influence on the number of rail breakage's can be seen. Much more rail breakage's occur under cold conditions (winter) than under warm conditions (summer).
It is assumed that the factors traffic load, material quality and temperature have a significant influence on the crack and breakage problem. However, these influences couldn't be quantified during this work. Therefore these nodes are omitted in the influence diagram and the following optimisation.
However, it is an important future work to include these nodes in the diagram and find a mathematical description of these influences. This will lead to an improvement of the modelling.
Assessing parameter values
Estimation of the P F interval and the standard deviation
One possibility to get information about the length of the P F interval is, to check the railway statistic if there is any crack reported twice; but classified into different failure classes. In the statistics this information was found for a couple of rail cracks that first had been classified as failure class 2b and later on as class 1. The survey of the time interval between these reported events leads to an average value of 1.68 years. This value can be claimed to be the time for the average P F interval between failure class 2b and failure class 1. However, there is a significant variance in the values. The standard deviation is 1.71 years. The length of the P F interval TPF= 1.68 years is the mean time that a crack needs for the propagation from class 2b to class 1. The value for the searched P F interval will in all circumstances be longer. This applies for the standard deviation of the P F interval as well. However, the values can be used for the estimation of the P F interval.
Palese and Zarembski (2001) has further found that the interval between the time when the defect grows to detectable size to the time when the actual failure is imminent is of the order of 10 to 50 mgt (megaton), depending on a number of track, traffic and environmental factors. On Dovrebanen there is an annual traffic load of about 4 mgt. This indicates that the average P F interval should be between 2.5 and 12.5 years. Experts from JBV were also interviewed to assess the P F interval length. They estimated the P F interval to be 5 years in average.
Based on this a length of the average P F interval (µ) of 5 years (60 months) was used. The standard deviation (d) was assumed to be 3 years (36 months).
Failure probability ultrasonic measuring: q
Number of derailments
Other values for the optimisation model
Unfortunately there is almost no information about the required figures in Table 5 in the Norwegian statistics. The only indication from the statistics is the "method of detection" of cracks and breakage's.
Assessing costs figures
For the ultrasonic inspection JBV hires the measuring car from an American company that operates in the Nordic countries. The cost for one shift is 60,000 NOK. In addition with costs for personnel, an amount of 100,000 NOK was used in the optimisation analysis. At least two shifts are required for a typical line in Norway.
For the costs of derailments Palese and Zarembski (2001) refer to the Federal Railroad Administration (FRA) statistics. The entire range of rail defects varies from 1.6 million NOK to 11.2 million NOK depending on defect type, with an overall average on the order of 3.2 million NOK. But this is FRA reportable cost only. The actual cost of the derailment, which could include loss of lading, train delays or train rerouting, can double that amount. In addition to these economic values we may also have cost of killed and injured persons. In Norway statistics shows an average of 0.2 fatalities per derailment. With a "value of one statistical life" of 20 million NOK as used in Norwegian in tranportation analyses, the "total" cost of a derailment is set to 15 million NOK.
The costs for renewal and other damages were estimated together with experts from JBV. The figures are summarized in Table 6.
4. Optimisation resultsThe influence diagram in Figure 2 is quantitatively modelled in an EXCEL spread sheet. This enables easy optimisation of the inspection intervals, as well as sensitivity analyses. Figure 7 shows the total cost for diferent inspection intervals for Doyrebanen. The current inspection interval is 24 months. From Figure 7 we see that the total costs decreases as the interval become shorter. The minimum cost is reached at approirnately ten months i.e. a duplication of the inspection frequency up to one measuring per year could be recommended. In this case a saying of approx. 300,000 NOK (35,000 Euro) can be expected. Similar optimisation was carried out also for Bergensbanen and Nordlandsbanen.
5. Conclusions and suggestionsThe present study has provided a simplified model for o~sation of ultrasonic inspection. The elaborated influence diagram was a suitable tool fbr the work and can be a basis for the future work. The mathematical optin iisation model was established with the basis from the influence diagram The ultimate result of the optimisation is the inspection interval should be reduced from the current practice of 24 months to 12 months for the lines being analysed. Yearly savings of 30 40 thousand Euro could be expected per line due to the new maintenance strategy. For the entire Norwegian network this could give savings of more than hundred thousand Euro.
For JBV such models are very helpful because:
Another important factor is the ultrasonic inspection failure probability, q. This parameter has large impact on the cost figures. In addition to get better estimates for this parameter it is also important to reduce the failure probability. There are several means that could be considered:
AcknowledgmentPart of this work has been supported by the European Commission under the EU-project ProM@in (http://promain.server.de). Thanks also to Thomas Welte who has carried out much of the modeling and analyses during his project work at the Norwegian University of Technology and Science (NTNU).
In the following we will describe the method used for calculating., the probability that a potential failure is not detected by ultrasonic inspection. There are two main sources for not detecting a potential failure in due tinie; i) the inspection interval is to long compared to the P F interval, and ii) the quality of the inspection is to low to detect a potential failure. The following quantities are defled:
|TPF||PF interval (random variable).|
|xPF||Probability distribution function of TPF|
|q||Failure probability of one inspection, i.e. the probability that a given run fails to detect a potential failure|
|qC||Common cause part of q|
|ql||Independent part of q|
The probability that the inspection strategy fails to reveal a potential failure before a critical failure occurs could be found by the low of total probability:
where Qt(t,q,t) is the probability of not detecting a potential failure given that the P F interval, TPF, equals t. In order to calculate Qt(t,q,t) we observe that when TPF = t, then number of possibilities to detect a failure equals n or n + 1 where n = int(t/t,) where int(.) is the integer function. The probability that we will have n + 1 possibilities equals t/t - n and thus the probability that we will have n possibilities to detect a potential failure equals n +1 - t/t. Since the probability that a given inspection fails to detect a potential failure equals q, Qt(t,q,t) could easily be obtained by:
if the inspections could be considered statistically independent. However, the assumption that inspections are independent does not seem realistic. A more realistic assumption would be to assume that the failure probability of one inspection is given by:
|q = qc + ql||(3)|
whcre qc represents common cause failures duo to hystematic failures such as low coverage, and ql represents the failure probability due to specific conditions for one run, e.g. inadequate velocity of the measuring wagon, human errors etc.
Assuming that the failure probability of one inspection could be divided into a common and an independent part as shown in eq. (3) we calculate the total failure probability of the inspection strategy as:
Q0(t,ql,xPF) could easily be approximated by an EXCEL spreadsheet function. In the present study xPF) is assumed to be a gamma distribution with mean µ and standard deviation s.
there is also probability that a potential failure is not revealed during an inspection, the inspection interval should be shorter than the average P F interval. In Appendix A a model to calculate the failure probability in this situation is presented. A prerequisite for using the P F intervals in maintenance planning is that a failure is alerted by some degradation in performance, or some indicator variable is alerting about the failure. Such a variable could be vibration, cracks, increased temperature etc. In this special study this indicator is "cracks".