Predictive modelling involves using a model of a process, usually a computer model, to predict a likely outcome. Model predictive control (MPC) takes this further and uses a dynamic model to calculate how the process should be managed.

It can be used in a railway setting to predict, for example, the rate of wear on rails. Given data on the nature of the rail, the nature of the traffic and experience of previous similar rails subject to similar traffic, maintenance engineers are able to plan to replace rails before the wear reaches critical levels.

MPC has been used since the 1970s in industrial control systems. Such systems monitor many different parameters at key points in the process, compare the data with the ideal figures and make adjustments. The key thing about MPC that differentiates it from conventional control systems is that every adjustment that can be applied to a given situation is modelled and the best solution applied, rather than the easiest, the usual or the one the operator has used before.

MPC on the railways

Since the 1990s MPC has been applied to railway control systems, automatically making small adjustments to train departure times and speeds to keep the network as a whole working to schedule. One of the earliest implementations of this technology was installed by Invensys on London Underground’s Central Line in the 1990s. A later iteration is now being applied to the Victoria Line and the Singapore Metro’s east / west and north / south lines. There is a bidding process currently underway to select a suitable train control system for the central section of the London Underground network.

“Predictive modelling involves using a model of a process, usually a computer model, to predict a likely outcome.”

Automatic train regulation (ATR) was developed by Invensys working with Zircon Software, specialists in software development for the aerospace, defence and transport industries, and based on the work of Dr Tam Taskin at Birmingham University.

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The earliest versions suffered from what Invensys manager Richard Hathaway described as an "over-academic user interface". Subsequently a lot of work has gone into giving the controllers a more useful screen that tells them what they need to know, without bombarding them with too much information.

ATR is suited to small networks such as city metros because it operates on quite a short time scale.

In that kind of operation the most useful thing ATR can do is improve the service in the next ten minutes, according to Hathaway. In predictive modelling this is referred to as the "moving horizon approach". Looking further ahead things can become more unpredictable.

When designing an ATR system there are different outcomes to consider and allocate importance to. When Invensys installed the Central Line system, the primary focus was on improving the passengers’ perception of the service. That led to a system which put more emphasis on trains arriving and departing than on overall speed, mainly due to passengers finding waiting on a platform more frustrating than being on a slow train. More recent versions have focussed more on reducing energy consumption.

Expanding MPC to mainlines

ATR works well on single lines or relatively small self-contained networks, but it isn’t designed to cope with Intercity or transcontinental operations. As yet, nothing is, but academics at Delft University in the Netherlands and elsewhere are working on it.

“Since the 1990s MPC has been applied to railway control systems, automatically making small adjustments to train departure times and speeds.”

In 2001 professor B de Schutter and researcher TJJ van den Boom published a paper on MPC called "Model predictive control for railway networks", outlining their work. The paper explains how moving horizon MPC uses discrete-time models and how these are applicable to, for example manufacturing systems where a finite number of resources shared by several users (or jobs) lead to a particular outcome. Such systems are non-linear, which means several processes can occur simultaneously with no effect on each other providing they are all complete on target. Railway Networks are a lot more complex. Using moving horizon methods as in ATR can be trouble if it is applied to larger systems.

The conundrum they set out to solve is how best to return a network system to normal working following some kind of disruption. And "best" in this case focuses on cheapest, rather than ATR’s fuel saving or passenger perception.

They take the case of a train known to be running late towards an interchange. There maybe several hundred passengers a proportion of whom are planning on making connections with other trains. The controller has the option of delaying the departure of those other trains, or not. The options are complex, if they are not delayed a lot of passengers are annoyed and maybe eligible for compensation. If they are delayed, will they be able to make up time, or will their passengers also be late? Even if they can all make up time on their runs, how will their late running on the initial stage affect other trains using the same line? Factor in compensation payments to passengers and possible penalty payments to network operators and it all gets very difficult.

To help analyse this, de Schutter and van den Boom define hard and soft synchronisation constraints on the network. The former is something strictly linear that cannot be broken, the most obvious example being that train A cannot leave before it has arrived. Soft constraints can be broken, but at a cost. Train B should not leave until arrive x minutes after train A arrives to allow passengers to transfer, but in some circumstances it might be better to ignore that constraint.

Assistant Professor at Delft, Dr Rob MP Goverde, said "Over the last few years several advances have been made on the mathematical modelling and data mining of train detection data, to allow fast and reliable forecasts on large-scale networks."

“ATR is suited to small networks because it operates on quite a short time scale.”

He added that the season would be extended and combined in "a model-predictive control framework".

"Major challenges are establishing an online connection to train positioning data, filtering this data into accurate travel time forecasts in real-time, finding optimal control decisions with respect to delays and disruptions, and gaining the trust of dispatchers in the software," he added.

In addition to Delft, several universities in Switzerland and Germany are engaged on this state-of-the-art research. The Delft team was granted more research funds last year and has, since April 2010, had two PhD students working on the MPC model with the aim of running a prototype within four years.