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Artificial Neural Networks: Applications in Chemical Engineering

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Modeling and Simulation in Chemical Engineering

Part of the book series: Heat and Mass Transfer ((HMT))

Abstract

Traditional approaches to modeling real chemical engineering processes are based on fundamental chemical and physical laws, which include nonlinear algebraic and differential equations. From a computational point of view, these equations have some difficulties with regard to the numerical methods used for their approximation, as well as with the achievement of the desired accuracy of the calculations.

In recent years, there has been a growing interest in the application of the Artificial Neural Networks (ANNs) method to solve a number of problems in the field of chemical engineering related to fault detection, signal processing, modeling, and control of chemical and biochemical processes in which traditional modeling methods have difficulty and it is even impossible to develop physical models with acceptable errors.

Their main advantage is that they work only with data on the input and output values of the process parameters. One model can be used to generate multiple outputs. Once the neural network model is adequately trained and validated, it is able to make predictions for new data about the input values of process parameters that were not used in the development of this model.

This chapter presents the main characteristics of ANNs, the choice of architecture, the process of training and validation of ANN models, as well as several types of ANNs, such as feed-forward nets, recurrent nets and radial basis function nets and combined models with examples of applications in chemical engineering.

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Abbreviations

b :

Vectors with values of biased neurons for the hidden and output layer

B :

A matrix of weighting coefficients represented by connections from an input layer to a hidden layer

c:

A vector that centers each RBFN function in the input space

C :

A matrix of weighting coefficients represented by connections links from a hidden layer to an output layer

D :

A matrix of weighting coefficients for the recurrent connections from the output layer at a time t − 1 to the inputs of the hidden layer at a time t

E :

Error of estimation between measured and calculated values of the outputs

f(⋅):

Nonlinear function

g :

Transfer function or activation function

h :

A general signal in which the weighted signals are summed up to a given neuron

I :

Neural network inputs

J :

Standard least squares function

N :

Number of data samples

O :

Neural network outputs

u :

Vector with input values

v :

Common input of each neuron

w :

Weighting coefficients of the connections between input to the hidden layer and hidden layer to the output layer

x :

Vector with values of the hidden layers

y :

Vector with measured values of the outputs

\( \hat{y} \) :

Vector with the values of the outputs predicted (calculated) by the model

z :

A time shift

Z :

A set of the values of the inputs and outputs

ε :

Vector of model error prediction

\( {\hat{\Phi}}_{\Psi_1{\Psi}_2} \) :

Normalized cross-correlation between two variables (time series) Ψ1 and Ψ2

φ(⋅):

Activation functions (transfer functions) of neurons in the hidden and output layers

θ :

Vector with parameters of nonlinear IRN model

σ :

“span” parameter in radial basis function network

ζ :

Positive scalar function

h :

For hidden layer

i :

For neurons (nodes)

j :

For neural network inputs

o :

For the output layer

t :

For time

ANN:

Artificial neural network

ERN:

Externally recurrent network

IERN:

Internal-External recurrent network

IRN:

Internally recurrent network

MAPE:

Mean absolute percentage error

R:

Linear correlation coefficient

RBFN:

Radial basis function network

RMSE:

Root mean square error

RNN:

Recurrent neural network

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Authors and Affiliations

  1. Institute of Chemical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Elisaveta G. Kirilova

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  1. Elisaveta G. Kirilova
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Correspondence to Elisaveta G. Kirilova .

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Editors and Affiliations

  1. Institute of Chemical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Christo Boyadjiev

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Kirilova, E.G. (2022). Artificial Neural Networks: Applications in Chemical Engineering. In: Boyadjiev, C. (eds) Modeling and Simulation in Chemical Engineering. Heat and Mass Transfer. Springer, Cham. https://doi.org/10.1007/978-3-030-87660-9_6

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