(183r) An Artificial Neural Network Approach for the Identification of Stochastic Models of Travelling Traders’ Exchange Process

Authors: 
Huang, C., University College London
Piccione, P., Process Studies Group, Technology & Engineering, Syngenta
Cattani, F., Process Studies Group, Technology & Engineering, Syngenta
Galvanin, F., University College London

An
Artificial Neural Network Approach for the Identification of Stochastic Models
of Travelling Traders’ Exchange Process

 

C.
Huang1, P. M. Piccione2,F. Cattani3,
F. Galvanin1,*

1Department
of Chemical Engineering, University College London

Gower
Street, London WC1E 6BT (UK)

2
Process Studies Group, Technology and Engineering,
Syngenta, Breitenloh 5, CH-4333 Münchwilen, Switzerland

3
Process Studies Group, Technology & Engineering, Syngenta, Jealott’s Hill
International Research Centre,

Bracknell,
Berkshire, RG42 6EY (UK)

*
f.galvanin@ucl.ac.uk

The
Travelling Traders’ Exchange Process [1] (TTEP) is a stochastic process formulated
to study the nature and insights of the dispersion and redistribution of a physical
property (money) as a consequence of random sequentially-occurring exchange
events between traders. The TTEP models are developed to study how the money
distribution to traders will evolve over processing time and the properties of steady
state that the system will eventually achieve given different model
constructions. The analysis of stochastic model realisations obtained from the simulation
of TTEP models is essential for process understanding, control and
optimisation.

Stochastic
simulations have been executed using a simple 1-D TTEP model in which operating
and initial conditions are established including money transfer coefficients, trader
population and initial money distribution. Simulation results at steady state
in terms of money distributions to traders involve distinct output patterns
that are influenced by the values of operating variables in the model. Figure 1
presents three possible money distribution patterns (A, B and C) observed at
steady state. The major challenge is to select appropriate regression models to
analyse the evolution of money distribution in time and to represent and
classify the distribution patterns obtained from TTEP stochastic simulations.

Artificial
Neural Networks [2] (ANNs) are versatile, self-adaptive and scalable tools to
tackle large and highly complex data analysis tasks. Depending on the amount of
data available for network training, ANNs are likely to outperform other
Machine Learning techniques on even complex tasks [3]. It is interesting to
link this powerful tool to the problem of identifying the nature of the outcomes
of TTEP stochastic simulations. ANNs enable elucidating the connection between
inputs and outputs to the process which is otherwise extremely complex to analyse
in the case of stochastic systems.

Conventionally,
distribution patterns are analysed via classical regression techniques after the
simulation terminates and the distribution pattern has become an observable
output [4]. This manual manipulation presents efficiency and precision issues: (i)
The pre-set simulation time must be large enough as to insure that steady state
has been reached; (ii) The selected regression models may have less estimate
precision in regression analysis.

The
objective of this work is to develop a computational framework to recognise and
classify money distributions captured in TTEP stochastic simulation processes using
ANN techniques so as to assist the regression model identification procedure.

To
validate the neural network, firstly, the network layers are established and
neurons in each layer are initialised by random weights and biases. Then, a set
of training data are produced to give network training so as to adjust the
values of weights and biases of neurons in network layers. After training, the network
will be able to recognise and classify the data configuration captured at each
sampling point and correctly tell if the system achieves steady state and needs
to commence further investigation. With well-trained ANNs, we may move to the
stochastic model investigation section. The entire model investigation process
comprises three steps that are presented by Figure 2. In the first step
stochastic simulations are executed using TTEP model with given input
variables. After the simulation process, samples of money distribution are collected
at different time points and a database will be built and sent to the ANN for
analysis. In the second step, the sample is recognised by the ANN, verifying that
steady state has been detected and distribution pattern of the sample has been
classified into classes (A, B, C, etc.).  The process then moves to the next step.
In the third step, the corresponding regression model is selected based on the category
classified in step 2 to drive the choice of the most suitable regression model
in the identification procedure. The integration of simulation and
identification facilitates automatic investigation on the TTEP stochastic
model.

The
development of ANNs from stochastic models provides an efficient way to
identify the nature and insights of stochastic models with high precision and
accuracy. Future work aims at extending the applicability of the ANNs approach
to TTEP models with higher complexity regarding model structure and money
exchange mechanism, so that the trained ANNs will be capable of identifying
data configurations and distribution patterns independently from the stochastic
model structure.

       

   Figure 1. Possible money distribution patterns obtained at steady state by applying different money transfer coefficient values in model simulation.Figure 2. Flowchart of stochastic simulation, automated money distribution pattern classification and regression model identification.

  References

[1]

C. Huang, P. M. Piccione, F. Cattani and F. Galvanin, “A two-layer identification strategy for the development of stochastic models of the travelling traders’ exchange problem,” in 27th European Symposium on Computer Aided Process Engineering, Barcelona, 2017.

[2]

S. Samarasinghe, Neural Networks for Applied Sciences and Engineering, Boca Raton: Auerbach Publications, 2006.

[3]

A. Géron, Hands-on Machine Learning with Scikit-Learn and TensorFlow, Sebastopol: O'Reilly Media, 2017.

[4]

D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications, New York: Wiley, 2007.