Railway vehicle modelling using neural networks · 4- NEURAL NETWORKS Modelling of lateral vehicle responses PRINCIPLE Structure composed of calculation units (neurons) Non-linear

SNCF RESEAU, Direction Ingénierie & Projets (I&P)

S. KRAFT, J. CAUSSE, F. COUDERT (LVE)

21 Juin 2016, Paris

0 /21

13/06/2016

Railway vehicle modelling using neural networksMATLAB EXPO 2016

SNCF RESEAU, Direction Ingénierie et Projets (I&P)S. KRAFT, J. CAUSSE, F. COUDERT (LVE)21 Juin 2016, Paris



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CONTENT

1- INTRODUCTION

2- VEHICLE MODELLING

3- BLACK-BOX MODELLING

4- NEURAL NETWORK

5- RESULTS

6- CONCLUSIONS



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1- INTRODUCTION

Assessment of track geometry defects

Running safety

Passenger comfort

Infrastructure management

Speed reduction

Maintenance work

Track assessment

Track geometry recording train

Track geometry parameters

Track maintenance

Alignment (AL) Longitudinal Level (LL)

Cross-LevelGauge



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1- INTRODUCTION

TRACK GEOMETRY – VEHICLE RESPONSE CORRELATION

Low correlation between geometry parameters and vehicle responses (DYNO train project)

ASSESSMENT OF VEHICLE RESPONSES

Identification of critical defects

Improved track maintenance

Vehicle-based track assessment

Vehicle ResponsesTrack geometry and design

bogie

Car body

forces

accelerationwheelset

Cant and curvature

Defect amplitude and length



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Characteristics of vehicle-track system

NONLINEARITIES AND DISCONTINUITIES

Lateral Dynamics

Suspension elements

Wheel-rail contact

VARIABLE OPERATION CONDITIONS

Speed

Track Design (Curvature, Cant)

Track quality level

Nonlinear Suspension


Wheel-rail contact



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Modelling approaches

PHYSICAL MODELLING (VAMPIRE®)

Multi-body model

Finite-element model

BLACK BOX MODELLING (MATLAB®)

Transfer function

System Identification Toolbox

Neural Networks Toolbox

Multi-body model Training and validation of black box model


Vehicle responseTrack geometry

Training

Validation



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Comparison of modelling approaches

Multi-body model Black-box model

System knowledge

Model complexity

Computing time

Nonlinearities

Model precision

Model selection criteria


Vehicle



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3- BLACK BOX MODELLINGStudied approaches

EMPIRICAL TRANFER FUNCTON

Strictly linear model

Superposition of SISO models for each track parameter

Transfer function model

Vertical responses Lateral responses

MODEL VALIDATION

Comparison with multi-body model

Result of model validation



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NONLINEAR ARX MODEL

Linear difference equation with nonlinear function

Vertical responses Lateral responses

MODEL VALIDATION

Comparison with multi-body model

Result model validation

3- BLACK BOX MODELLINGStudied approaches

Nonlinear ARX Model



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4- NEURAL NETWORKSModelling of lateral vehicle responses

PRINCIPLE

Structure composed of calculation units (neurons)

Non-linear black-box modelling

NEURON

The neuron is composed of the input vector, the

weighting factors, the bias and the transfer function

(linear or non-linear)

The parameters are identified using an optimization

algorithm

ARCHITECTURE

Number and connections of neurons

Arrangement of the neurons in layers

Network without feedback (feed forward) or with

feedback (recurrent)

Neural network



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NETWORK TYPE

NARX: recurrent dynamic network

STRUCTURE IDENTIFICATION

Systematic variation of structure

parameters

TRAINING

Identification of network parameters

Minimization of cost function

DATA SETS

Representative teaching data

Type Structure Training Data sets

4- NEURAL NETWORKSModelling of lateral vehicle responses

Neural Network Identification

Training of NARX network



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COMPLEXITY OF STRUCTURE

Representation of system dynamics

Avoidance of « over-fitting »

STRUCTURE PARAMETERS

Number of layers

Number of neurons in layers

Number of delays

STRUCTURE OPTIMISATION

Systematic parameter variation

Optimization algorithm

Systematic variation of structure parameters

Cost function


4- NEURAL NETWORKSStructure identification


Number of delays

Num

ber

of

neuro

ns



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CRITERION OF NARX MODEL PRECISION

Distance between model xmodel and

measurement xmeas

Least-square cost function

Statistical values (Maximal, standard

deviation)

OPTIMIZATION ALGORITHM

Minimization of cost function

Local algorithm

Global algorithm


4- NEURAL NETWORKSNetwork Training


Cost function between model and measurement

Maximal values per section

Measurement

NARX Model

Measurement

NARX Model



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OPTIMAL TRACK LENGTH FOR TRAINING

REPRESENTATIV TRAINING DATA


4- NEURAL NETWORKSSelection of training data sets




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OPERATION CONDITIONS

Speed range

Vehicle type

Track design parameters

MODELLING APPROACH

Unique model for all

operation conditions

Multi model

NARX MULTI: Multi model as a function of curvature


4- NEURAL NETWORKSConsideration of operation conditions




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MODEL TYPE

NARX Unique

NARX Multi

TRAINING ALGORITHM

Local

5-RESULTSTest cases

Model Type Track design Speed LTrain Lval

NARX Unique

NARX Multi

All 160 km/h

160 km/h

160 km/h

Straight track

Curve

C = 0.4 - 0.6

C = 0.9 - 1.1

6km 45km

Cost function

134%

139%

51%

98%

Vehicle: TGV

Training data: random

Conclusion

not sufficient

6km 45km

sufficient

Vehicle

Locomotive

NARX Multi

160 km/hC = 0.15 - 0.3

68%4km 9km

TGV

140% not sufficient, high variability6km 48km

4km 6km

sufficient

not sufficient

Straight track

Locomotive

61%

sufficient

sufficient

C = 0.9 - 1.1 84% sufficient3km 3km

3km 3km

6km4km

Vehicle: Locomotive

Training data: random



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5-RESULTSExample: Cost function evaluation

kilometric position [km]

abl[m

/s²]

ab

l[m

/s²]

COMPARISON NEURAL NETWORK – MULTI BODY MODEL

Lateral bogie acceleration abl

Cost function at 98%

Maximal values within safety margin

Cost function = 98% Maximum values




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5-RESULTSExample: Optimal track length

LENGTH OF TRAINING DATA SET

Variation of training length from 1 to 10 km

Random data set

MODEL VALIDATION

Convergence of cost function at 3 km length

Cost

function[%]

Training

length [km]

Convergence of cost function

Training length

Training

Validationkilometric

position

Model

Analysis case



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5-RESULTSExample: Creation of random data sets

DATA ASSEMBLING

Data from 3 lines used

Smoothing between data

segments

DATA SECTIONS

Sections of 300 m length

RANDOM DISTRIBUTION

Track quality

Curvature

Track quality distribution

Curvature distribution

Random distribution of curvature and track quality


Sta

ndard

devia

tio

n[k

m]

Curv

atu

re [

km

]



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6- CONCLUSIONS

VEHICLE-BASED TRACK ASSESSMENT

Identification of critical defects

Improved maintenance strategies

ADVANTAGES AND DRAWBACKS OF BLACK-BOX MODELLING

Benefits of black-box models (no system information required, low

simulation time, easy use)

Difficulty of modelling nonlinearities of lateral vehicle dynamics

USE OF NEURAL NETWORKS

Modelling of lateral vehicle responses is possible

Model precision depends strongly on operation conditions

Use of multi-models as a function of track design

Further work is required

SNCF RESEAU

S. KRAFT, J. CAUSSE, F. COUDERT (I&P LVE)

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6- CONCLUSIONS

STRUCTURE OPTIMIZATION

GLOBAL OPTIMIZATION FOR PARAMETER IDENTIFICATON

MULTI-MODEL USING FUZZY LOGIC TOOLBOX

“GREY BOX” MODELLING USING PHYSICAL KNOWLEDGE

Ongoing work and perspectives

Curvature [1/km]

« Membership function »

FUZZY logic for multi-model Grey-box model

NARXNARXNARX



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THANK YOU FOR YOUR ATTENTION

Documents

Railway vehicle modelling using neural networks · 4- NEURAL NETWORKS Modelling of lateral vehicle responses PRINCIPLE Structure composed of calculation units (neurons) Non-linear