Predictive and probabilistic gauging: The shoehorn effect

Gauging has advanced rapidly in recent years from a process where vehicle gauges and structure gauges were simply profiles that must not be exceeded. Writes Dr David M Johnson, director, DGauge Ltd

Most British rolling stock is now gauged ‘absolutely’; the swept envelope of the vehicle is modelled by computer and compared with a profile measurement of the infrastructure considering the operating conditions at the particular location, for all structures along a route. The space between the vehicle envelope and the structure is known as the clearance, and must be at least as large as that required by Railway Group Standards. As a result of using these advanced techniques, it is possible to run larger trains than the rail network was originally designed for.

This is because traditional vehicle gauges require the gauge line to include an allowance for the maximum vehicle suspension travel which would normally occur at maximum speed and cant deficiency. Even if a vehicle is operating at maximum speed, operating at the extreme of cant deficiency only occurs at relatively few locations. On straight track the amount of the maximum swept envelope occupied by the vehicle is quite small. Absolute gauging develops a swept envelope appropriate to local operating conditions and in the case of straight track would be smaller than that on a curve. Accordingly, the hole required for the train to pass would be smaller.

Traditional gauging methods

Such calculations originate from hand-calculation methods developed in the 1980’s to enable the introduction of rolling stock with air suspension (which have greater suspension movement than metal-sprung vehicles) onto routes that had insufficient indicated space when tested by the traditional gauging methods. BASS501, produced by British Rail, was a seminal document which defined a method that considered both the effect of curving forces and movements associated with the vehicle travelling over imperfect track. More recently, dynamic simulations using VAMPIRE® software allow even more realistic modelling.

Today, gauging calculations can only be undertaken using gauging software which is used to compare detailed profiles of the vehicle with the infrastructure through which it passes. In Great Britain, ClearRoute™ software has been used for many years to perform such calculations to great effect and its introduction in the 1990’s provided the opportunity to assess the true capability of the railway network and allow the introduction of trains such as Pendolinos and 9’6” container traffic.

Conservatism in the calculations

However, when (Network Rail’s) National Gauging Database was introduced, it became clear that some rolling stock was running in locations where clearances were indicated to be sub-standard or foul. The accident free history of the running of such rolling stock indicated that this was not likely to be a true clearance issue, but one of conservatism in the calculations. More detailed examination revealed the origin of such conservatism as being in the tolerances that are routinely applied as part of the gauging process.

Whilst simulation provides a good indicator of vehicle movement under various track conditions, the vehicle / infrastructure relationship is by no means a reflection of the title ‘permanent way’. Track moves over time, rails and wheels wear, suspension parameters change and loading conditions vary – all of which affect the clearance between a train and a structure. To accommodate such variations, tolerances are included to ensure that indicated clearances are ‘worst case’. These tolerances are applied additively and in the ‘worst’ direction. At the top of a typical vehicle, such tolerances may amount to 70mm. In practice, this means that if a true clearance of 100mm exists, simulation could indicate 30mm clearance and much effort would be applied to maintain a regime of Special Reduced clearances.

Unlikely aggregation of tolerances

Aside from such analysis indicating that trains may be unable to pass infrastructure, the more general view is that we are providing clearance beyond that required to accommodate rare events that might happen simultaneously. We are considering, for example, that track might be at one extreme of its positional tolerance, at the same time as installed cant, wheel wear and maximum sway also align in the same direction. If we are considering passing clearances, we must also assume that adjacent tracks are forced towards each other, albeit with a small allowance to reduce the conservatism that this introduces. Such aggregation of tolerances is, at best, unlikely.

However, the concept of ‘unlikely’ does not sit well in our railway world and particularly when it comes to determining whether a train will strike the infrastructure. But whether we like it or not, likelihood is a reality because we are dealing with statistically derived parameters yet deluding ourselves that they are absolutes. We must provide 100mm clearance, period.

Uncertainty analysis

Other engineering disciplines have taken a more enlightened approach and considered the probabilities of an event occurring. These industries are not benign – nuclear, aviation, aerospace, automotive, etc. The consequences of risk in these industries is equally, if not more, serious than in our own. And even if we do not recognise it, in gauging we are using statistical measures in our calculations. Specifically, we apply a maximum suspension movement of the vehicle. Such is the dependency of this factor on, say, track irregularities that might develop, it is extremely difficult to provide a reasonable value of movement that would not be exceeded. However, in recognition of this, the statistical measure of maximum movement being the mean movement (due to curving forces) plus 2.12 standard deviations is used. Thus, we would expect a vehicle to exceed this movement envelope in approximately 3% of situations (it is not a ‘normal’ distribution). And yet we use this value, add the tolerances, and check that we have met a 100mm clearance, precisely.

In recent years, this approach has been questioned. RSSB commissioned two research projects (T373 – “Uncertainty in Structure Gauging” and T670 – “Investigation of the accumulative effect of vehicle tolerances on gauging”, which specifically investigated the potential of “uncertainty analysis” as a means to aggregate tolerances and allowances in a statistically valid manner. The process of uncertainty analysis considers how individual tolerances many vary, and how they are aggregated as part of a system. Some parameters affect the swept envelope of a vehicle directly; others act to change the dynamic behaviour of the vehicle, with a different effect on its swept envelope. If we consider each parameter, and there may be many, we can look at the probability distribution of its likely magnitude. Some may linearly relate to component life (for example radial wheel wear), others may relate to a ‘normal’ distribution (for example build tolerances). Others may possess unique distributions (such as the movement generated from track irregularities). There is no simple way of evaluating the statistical aggregation of such a diverse range of parameters, particularly when some affect the system directly and others affect it indirectly.

Greater understanding of railway gauging

As part of an academic exercise, the author constructed a sophisticated gauge modelling platform based upon best practice in modelling the various component subsystems that comprise the gauging system. These included models for structure, track, rail, wheel, bogie and body with new models developed for pantographs and the overhead line electrification (OLE) system. Rather than use a conventional ‘rule’ based approach to gauging, the platform is intrinsically linked to a ‘Monte Carlo’ event generator which can generate ‘events’ where all tolerances are within their prescribed bounds, and which occur within their own probability distribution. Coupled with rapid calculation of clearances it is possible, for example, to undertake 10,000 or more simulations and quickly generate a composite probability distribution of the resultant clearances that would occur over this representative lifetime.

For example, the results of such a simulation for Liverpool Street Platform 12 indicate that although tight, only extreme events would lead to a foul clearance developing. By managing such extreme events, there would be no need to reach for the angle grinder and remove another section of the passenger / train interface.

The ‘academic exercise’ has now been developed into a more robust software system, known as PhX rail™, which is accredited by Network Rail. It is in regular use providing a much greater understanding of railway gauging, and releasing a further tranche of space in our infrastructure that is reducing the cost of electrification and new train introduction or cascade.