Analysis of Big Data Streams to Obtain Braking Reliability Information for Train Protection Systems Prof. Dr. Raphael Pfaff Aachen University of Applied Sciences pfaff@fh-aachen.de www.raphaelpfaff.net @RailProfAC July 2013, 2017 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 1 / 25
User: Infrastructure Manager Executive Henry Job: ETCS Expert Employer: Infrastructure manager Challenges: Ensure safety, maintain or increase capacity Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 2 / 25
User: Infrastructure Manager Executive I need to ensure that signals are practically never overrun while at the same time, the load on my network increases every year. Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 2 / 25
ETCS provides the answer The moving block system helps to reduce headway. s b,max l bl S l t,1 s b,2 S l t,1 s b,2 s b,1 S Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 3 / 25
User: Infrastructure Manager Executive With the moving block system, I can improve infrastructure utilisation - I only need to find the braking curves! Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 4 / 25
What is a braking curve? ATP systems rely on braking curves to describe the train s braking capability. To supervise train velocity, ATP systems predict the future braking capability of the train 30 25 20 v/m/s 15 10 5 0 0 100 200 300 400 500 600 700 s/m Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 5 / 25
What is a braking curve? ATP systems rely on braking curves to describe the train s braking capability. To supervise train velocity, ATP systems predict the future braking capability of the train However, there is not the braking capability 30 25 20 v/m/s 15 10 5 0 0 100 200 300 400 500 600 700 s/m Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 5 / 25
What is a braking curve? ATP systems rely on braking curves to describe the train s braking capability. To supervise train velocity, ATP systems predict the future braking capability of the train However, there is not the braking capability Braking curves exhibit a randomised behaviour Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 5 / 25
How to obtain a braking curve? To obtain a braking curve, the stochastic behaviour of the system needs to be analysed, typically by help of a Monte Carlo Simulation. x 1 x 2 y = f (x) y x 3 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 6 / 25
Physical Modelling of the braking system Which parameters can be identified and which effect do they have on the braking distance? Brake pipe: propagation velocity, flow resistances, train length Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 7 / 25
Physical Modelling of the braking system Which parameters can be identified and which effect do they have on the braking distance? Brake pipe: propagation velocity, flow resistances, train length Distributor valve: Filling time, brake cylinder pressure Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 7 / 25
Physical Modelling of the braking system Which parameters can be identified and which effect do they have on the braking distance? Brake pipe: propagation velocity, flow resistances, train length Distributor valve: Filling time, brake cylinder pressure Braking force generation: efficiency, brake radius (for disc brakes), pad/block friction coefficient Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 7 / 25
Physical Modelling of the braking system Which parameters can be identified and which effect do they have on the braking distance? Brake pipe: propagation velocity, flow resistances, train length Distributor valve: Filling time, brake cylinder pressure Braking force generation: efficiency, brake radius (for disc brakes), pad/block friction coefficient Wheel/rail contact: rail surface, contaminants, slip,... Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 7 / 25
Physical Modelling of the braking system Which parameters can be identified and which effect do they have on the braking distance? Brake pipe: propagation velocity, flow resistances, train length Distributor valve: Filling time, brake cylinder pressure Braking force generation: efficiency, brake radius (for disc brakes), pad/block friction coefficient Wheel/rail contact: rail surface, contaminants, slip,... Also discrete failure events need to be considered Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 7 / 25
Brake pipe parameters Brake pipe parameters determine the distribution of the brake command along the train. Propagation velocity: Required: c 250 m s May be considered lower limit Flow resistances: Flow resistance in the individual wagons determine filtering behaviour of BP Train length: Non-random input parameter Wagon position: Distribution of braked mass in train and effective filling time influence overall braking distance Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 8 / 25
Distributor valve parameters Distributor valve parameters determine the effectivity of the brake command. Filling time t f : Brake modes P/R: (4 ± 1) s Brake modes P/R: (24 ± 6) s Uniform distribution (conservative) Brake cylinder pressure p C : Required: p C = ( 3.8 +0.2 0.1) bar Uniform distribution (conservative) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 3.6 3.7 3.8 3.9 4.0 4.1 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, for 2017 Train Protection 9 / 25
Braking force generation parameters Parameters of the braking force generation subsystem determine the propagation of braking effort between p C and wheel/disc. Efficiency Typical dynamic efficiency: η [0.75, 95] Depending on maintenance state Assumed uniform distribution Brake radius Systematic variation with pad wear, not relevant for block brakes Pad/block friction coefficient µ B Mean friction coefficient depending on v 0 Stochastic variation of instantaneous coefficient Normal distribution appropriate frequency 600 500 400 300 200 100 0 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 0.150 mu/1 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 10 Protection / 25
Wheel-rail surface parameters Rail surface: According to Hertzian theory Non-Hertzian contacts due to hunting Contaminants: Empirical estimation due to network Mostly dry braking curves simulated Slip: Curving motion, hunting impose 3D-slip on contact patch Adhesion budget gets used y/m 10 3 Adhesion area 5 0 5 1 0.5 0 0.5 1 x/m 10 2 F t/b = 10 kn F t/b = 15 kn F t/b = 20 kn F t/b = 25 kn F t/b = 30 kn Elliptical contact Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 11 Protection / 25
User: Infrastructure Manager Executive Looks like the simulation model is quite complex? Can we do this online? Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 12 Protection / 25
Approaches to obtain braking distance distributions Error-propagation: Conservative: assumes normal distribution for all parameters Complex: requires explicit function formulation and partial differentiation (Standard) Monte-Carlo-Simulation: Efficient (in terms of confidence): returns shortest (also asymmetric) confidence interval Inefficient (in terms of computational effort): For rare event ε 1, N 100 trials required ε Typical according to CSM: ε [ 10 7... 10 9] N 10 11 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 13 Protection / 25
Approaches to obtain braking distance distributions Error-propagation: Conservative: assumes normal distribution for all parameters Complex: requires explicit function formulation and partial differentiation (Standard) Monte-Carlo-Simulation: Efficient (in terms of confidence): returns shortest (also asymmetric) confidence interval Inefficient (in terms of computational effort): For rare event ε 1, N 100 trials required ε Typical according to CSM: ε [ 10 7... 10 9] N 10 11 ERA proposes to precalculate braking curves for limited number of train formations Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 13 Protection / 25
Approaches to obtain braking distance distributions Error-propagation: Conservative: assumes normal distribution for all parameters Complex: requires explicit function formulation and partial differentiation (Standard) Monte-Carlo-Simulation: Efficient (in terms of confidence): returns shortest (also asymmetric) confidence interval Inefficient (in terms of computational effort): For rare event ε 1, N 100 trials required ε Typical according to CSM: ε [ 10 7... 10 9] N 10 11 ERA proposes to precalculate braking curves for limited number of train formations Freight trains to be handled using braked weight and correction factor Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 13 Protection / 25
User: Infrastructure Manager Executive OK, basic Monte-Carlo is too complex to be calculated for each freight train. I fear a correction factor may be too conservative for well maintained wagon fleets. Are there any means to overcome this? Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 14 Protection / 25
ETCS: γ vs. λ braked trains Typical γ-braked trains: Multiple units, other fixed formations Braking curve specification via deceleration values Typical λ-braked trains: Any in-service configurable trains, especially freight trains Braking curve using correction factors (K dry,rst, K wet,rst ) to calculate based on brake weight Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 15 Protection / 25
ETCS: γ vs. λ braked trains Typical γ-braked trains: Multiple units, other fixed formations Braking curve specification via deceleration values Typical λ-braked trains: Any in-service configurable trains, especially freight trains Braking curve using correction factors (K dry,rst, K wet,rst ) to calculate based on brake weight The distribution of braking distances for freight trains of the same braked weight may be large: Empty/loaded selection vs. automatic load detection Maintenance state Tread vs. disc brake Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 15 Protection / 25
ETCS: γ vs. λ braked trains Typical γ-braked trains: Multiple units, other fixed formations Braking curve specification via deceleration values Typical λ-braked trains: Any in-service configurable trains, especially freight trains Braking curve using correction factors (K dry,rst, K wet,rst ) to calculate based on brake weight The distribution of braking distances for freight trains of the same braked weight may be large: Empty/loaded selection vs. automatic load detection Maintenance state Tread vs. disc brake It may be of advantage to run certain λ trains as γ trains Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 15 Protection / 25
Proposed solution (part 1): use importance sampling Importance sampling (IS) increases the probability of desired outcomes in Monte-Carlo-Simulations. Typical IS approaches: Stratification: select only relevant strata of the sampling range Scaling: Scale random variable Translation: Move random variable to more relevant part of sampling space Change of random variable: Replace random variable by one more likely to produce outcomes in the relevant range Adaptive approaches Effect: higher number of samples in region of interest Correction factor: Likelihood ratio L(y) = f(y) f(y) Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 16 Protection / 25
Application of IS to braking curves Change identified random variables, in the case at hand µ B 1400000 1200000 1000000 Basic MC IS: mu + l*sigma IS: k * sigma frequency 800000 600000 400000 200000 0 800 850 900 950 1000 1050 1100 1150 1200 1250 s/m Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 17 Protection / 25
Application of IS to braking curves Analyse for rare events, here braking distances in excess of 1100 m. N = 5 10 7 s n U p U n IS,1 p IS,1 n IS,2 p IS,2 1000 24400 4.89 10 3 2.27 10 6 1.14 10 2 3.11 10 5 1.77 10 3 1050 2 4 10 7 6.66 10 4 2.02 10 4 1.48 10 4 1.59 10 4 1100 0 0 115 2.04 10 7 419 7.50 10 6 1150 0 0 0 0 15 3.88 10 7 1160 0 0 0 0 7 2.05 10 7 1170 0 0 0 0 5 1.46 10 7 1180 0 0 0 0 4 1.16 10 7 1190 0 0 0 0 1 2.90 10 8 Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 18 Protection / 25
User: Infrastructure Manager Executive Well, this reduces the required Monte Carlo iterations by far, however handling braking curves for each wagon during brake assessment doesn t appear feasible. Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 19 Protection / 25
Solution (part 2): Connect the wagon subsystem The Wagon 4.0 offers sensing and connectivity as well as cloud representation. Sensing: Accelerometers to record deceleration, brake cylinder pressure sensor to measure braking force Connectivity: send braking data to cloud Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 20 Protection / 25
Solution (part 3): Big data analytics Big data analytics can be applied to separate train and wagon braking performance Record brake deceleration for wagons (in trains) in cloud Use big data analytics to derive individual wagon braking performance distribution Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 21 Protection / 25
MapReduce approach to braking curve estimation Data Map Reduce Result Data Map Reduce Result Data Map Data Map Reduce Result Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 22 Protection / 25
MapReduce approach to braking curve estimation Data Data Data Data Incoming Mapdata is mapped to individual train Using data from Map train list < k, t > Train number t servesmap as output key Group all data corresponding Map to one train Reduce Reduce Reduce Result Result Result Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 22 Protection / 25
MapReduce approach to braking curve estimation Data Map Reduce Result Data Data Map Map Worker nodes redistribute data All data for one Reduce train on one node Result Data Map Reduce Result Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 22 Protection / 25
MapReduce approach to braking curve estimation Data Data Data Data Map Map Map Map Monte-Carlo- Simulation Reduceof the remaining wagons braking performance Reduce Bayesian update of braking performance Store Reduce in < k, v >-Storage Result Result Result Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 22 Protection / 25
Simulated results of Big Data analysis 6 10 2 4 σ ˆσ σ 2 0 0 20 40 60 80 100 nbrakings 200 150 100 50 0 0 20 40 60 80 100 Wagon number Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 23 Protection / 25
User: Infrastructure Manager Executive Great, the approach to use Importance Sampling, IoT-technologies and Big Data analytics to gain the braking curves of each individually composed train improves our performance compared to running λ-trains. Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 24 Protection / 25
Thank you! Prof. Dr. Raphael Pfaff Rail vehicle engineering pfaff@fh-aachen.de www.raphaelpfaff.net Analysis of Big Data Streams to Obtain Braking Reliability Information July 2013, 2017 for Train 25 Protection / 25