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This paper describes artificial neural network (ANN) based prediction of the response of a fiber optic sensor using evanescent field absorption (EFA). The sensing probe of the sensor is made up a bundle of five PCS fibers to maximize the interaction of evanescent field with the absorbing medium. Different backpropagation algorithms are used to train the multilayer perceptron ANN. The Levenberg-Marquardt algorithm, as well as the other algorithms used in this work successfully predicts the sensor responses.

Evanescent field absorption (EFA) has been widely employed by some researchers for sensing of chemical and biological parameters over the past two decades [

EFA sensing mechanism utilized by fiber optic sensors is based on the absorption of the light carried by the evanescent field that coexists in the fiber cladding. In EFA fiber sensors the core is surrounded by an absorptive cladding that consists of a liquid [

In the last decade, ANNs became popular because they have ability to learn, fast real-time operation and ease of implementation features [

In this work, we have used the output power of an EFA fiber sensor made up a PCS fiber bundle. Then we have used a canonical variable incorporating the sensor's and absorbing dye's parameters to predict the response of the sensor by the aim of ANN because it can produce proper outputs for given inputs without any necessity to mathematical formulations between input and output data.

The sensing process based on EFA has been performed by using the arrangement in

The sensing element was a bundle that consists of five plastic cladding silica (PCS) fibers as shown in

For absorption measurements, Bromophenol Blue (BPB) indicator dye filled into the cuvette was used for absorbing cladding material. BPB is an indicator dye whose color is blue near pH 7 and varies by changing the pH. The monochromator was adjusted at a wavelength of 590 nm since the BPB solution has an absorption peak near this wavelength.

The sensor response (_{out}_{in}

The normalized frequency of the fiber is an important parameter for sensitivity purposes in EFA sensors because it plays an important role the amount of the evanescent field. Simply, the smaller the normalized frequency, the more evanescent field the fiber has. Therefore, in order to ensure a detectable interaction between the evanescent field and the indicator dye, the normalized frequency must be as small as possible. This can be achieved by the longer wavelength, the smaller fiber core diameter and the smaller relative refractive-index difference between the core and cladding [

Artificial neural networks (ANNs) are one of the popular branches of artificial intelligence [

Amongst the different types of connections for artificial neurons, feed forward neural networks are the most popular and most widely used models in various applications reported in the literature. They are also known as the multilayered perceptron neural networks (MLPNNs). In an MLPNN, neurons of the first layer send their output to the neurons of the second layer, but they do not receive any input back from the neurons of the second layer.

The general structure of an MLPNN is given in

The only task of the neurons in the input layer is to distribute the input signal _{i}_{i}_{ji}_{j}

There are many types of learning algorithms in the literature [

The LM algorithm is an iterative technique locating a local minimum of a multivariate function that is expressed as the sum of squares of several non-linear, real-valued functions and updates weight and bias values according to Levenberg-Marquardt optimization. The SCG which is a member of the class of conjugate gradient methods is a supervised learning algorithm for feedforward neural networks. The BFGS is one of the most powerful and sophisticated quasi-Newton methods and has the advantage over Newton's method that the second partial derivatives are not needed. The BR algorithm updates the weight and bias values according to LM optimization and minimizes a combination of squared errors and weights, and then determines the correct combination so as to produce a network that generalizes well. The CGP algorithm is a network training function that updates weight and bias values according to the conjugate gradient backpropagation with Polak-Ribiere updates. More details about the ANNs and learning algorithms can be found in the literature [

An MLPNN consisting of one input, two hidden layers and one output was used to predict the EFA sensor response. The input and output variables of the network are _{out}_{in}_{out}_{in}

The prediction performances of the ANN models are tested with five experimental points obtained from the sensor described in Section 2. The comparisons of the sensor responses and the network outputs are given in

If the percentage errors with respect to the experimental results are calculated for another performance comparison, it can be seen that the models with BR and LM have the smallest maximum percentage, errors being smaller than 2.0 (the maximum errors of the other models are smaller than 2.5).

For the discussion of influence of neuron numbers in the hidden layers on MSE and the sensor response, we trained the networks with the same neuron numbers and the same initial weights by using the model given in

An artificial neural network approach has been introduced in this paper to predict the response of an evanescent field absorption fiber sensor. Performance comparisons show that all of the neural models used in this work can predict the sensor responses with considerable errors. It is useful to note that, the neural network approaches can tolerate measurement errors. In conclusion, the artificial neural network approaches can play an important role in the design and development of intelligent sensors.

The arrangement for evanescent field absorption sensor [

The PCS fiber in the bundle (PCS200A, Quartz&Silice, France).

The geometry of the sensing region.

The sensor response (_{out}_{in}

General structure of an MLPNN.

An example of the networks proposed in this work.

Comparisons of the best and the worst ANN outputs with the sensor responses.

The training algorithms, artificial neuron numbers and resulted MSEs.

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LM | 1 | 3 | 5 | 1 | 1.85E-07 |

SCG | 1 | 2 | 5 | 1 | 9.98E-07 |

BFGS | 1 | 5 | 4 | 1 | 6.25E-07 |

BR | 1 | 2 | 2 | 1 | 1.10E-07 |

CGP | 1 | 4 | 4 | 1 | 3.55E-07 |

Comparisons of the sensor responses and the network outputs.

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0.7328 | 0.84 | 0.83269 | 0.84053 | 0.84139 | 0.83967 | 0.84130 |

0.4288 | 0.88 | 0.86355 | 0.85874 | 0.87051 | 0.85924 | 0.86277 |

0.2035 | 0.90 | 0.89983 | 0.90008 | 0.89909 | 0.90004 | 0.90058 |

0.1290 | 0.92 | 0.92003 | 0.91987 | 0.91944 | 0.91996 | 0.92030 |

0.0653 | 0.94 | 0.93748 | 0.93000 | 0.92248 | 0.93843 | 0.93089 |

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MSE | 0.04389 | 0.07333 | 0.05316 | 0.05762 | 0.05072 |

Performance comparisons of the networks for the model given in

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0.7328 | 0.84 | 0.83269 | 0.83450 | 0.83705 | 0.87837 | 0.83797 |

0.4288 | 0.88 | 0.86355 | 0.86220 | 0.85763 | 0.87837 | 0.85642 |

0.2035 | 0.90 | 0.89983 | 0.90040 | 0.89922 | 0.87837 | 0.89999 |

0.1290 | 0.92 | 0.92003 | 0.91970 | 0.91939 | 0.87837 | 0.91948 |

0.0653 | 0.94 | 0.93748 | 0.92560 | 0.92164 | 0.87837 | 0.92300 |

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MSE | 0.04389 | 0.0738 | 0.1125 | 0.9929 | 0.1129 |