railway vehicle modelling using neural networks · 4- neural networks modelling of lateral vehicle...
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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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
1 /21
CONTENT
1- INTRODUCTION
2- VEHICLE MODELLING
3- BLACK-BOX MODELLING
4- NEURAL NETWORK
5- RESULTS
6- CONCLUSIONS
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
2 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
3 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
4 /21
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
2- VEHICLE MODELLING
Wheel-rail contact
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
5 /21
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
2- VEHICLE MODELLING
Vehicle responseTrack geometry
Training
Validation
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
6 /21
Comparison of modelling approaches
Multi-body model Black-box model
System knowledge
Model complexity
Computing time
Nonlinearities
Model precision
Model selection criteria
2- VEHICLE MODELLING
Vehicle
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
7 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
8 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
9 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
10 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
11 /21
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
Type Structure Training Data sets
4- NEURAL NETWORKSStructure identification
Neural Network Identification
Number of delays
Num
ber
of
neuro
ns
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
12 /21
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
Type Structure Training Data sets
4- NEURAL NETWORKSNetwork Training
Neural Network Identification
Cost function between model and measurement
Maximal values per section
Measurement
NARX Model
Measurement
NARX Model
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
13 /21
OPTIMAL TRACK LENGTH FOR TRAINING
REPRESENTATIV TRAINING DATA
Type Structure Training Data sets
4- NEURAL NETWORKSSelection of training data sets
Neural Network Identification
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
14 /21
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
Type Structure Training Data sets
4- NEURAL NETWORKSConsideration of operation conditions
Neural Network Identification
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
15 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
16 /21
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
kilometric position [km]
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
17 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
18 /21
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
kilometric position [km]
Sta
ndard
devia
tio
n[k
m]
Curv
atu
re [
km
]
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
19 /21
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)
21 Juin 2016, Paris
20 /21
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
SNCF RESEAU, Direction Ingénierie & Projets (I&P)
S. KRAFT, J. CAUSSE, F. COUDERT (LVE)
21 Juin 2016, Paris
21 /21
THANK YOU FOR YOUR ATTENTION
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