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

- Conference: AIChE Annual Meeting
- Year: 2018
- Proceeding: 2018 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Monday, October 29, 2018 - 3:30pm-5:00pm

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

* *

*C.
Huang ^{1}, P. M. Piccione^{2},^{}F. Cattani^{3},
F. Galvanin^{1,*}*

^{1}*Department
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)*

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.

**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 |

[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. |