Application of the Spectrum Peak Positioning Technology Based on BP Neural Network in Demodulation of Cavity Length of EFPI Fiber Optical Sensor

doi:10.4236/jcc.2013.17016

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Journal of Computer and Communications, 2013, 1, 67-71

Published Online December 2013 (http://www.scirp.org/journal/jcc)

http://dx.doi.org/10.4236/jcc.2013.17016

Open Access JCC

Applicati on of the Spectrum Peak Position i ng Technolog y

Based on BP Neural Network in Demodulation of Cavity

Length of EFPI Fiber Optical Sensor*

Mengran Zhou, Mengya Nie

Anhui University of Science and Technology, Huainan, Anhui, China.

Email: [email protected]

Received October 2013

ABSTRACT

An Extrinsic Fabry-Perot Interferometric (EFPI) fiber optical sensor system is an online testing system for the gas den-

sity. The system achieves the measurement of gas density information mainly by demodulating the cavity length of EF-

PI fiber optical sensor. There are many ways to achieve the demodulation of the cavity length. For shortcomings of the

big intensity demodulation error and complex structure of phase demodulation, this paper proposes that BP neural net-

work is used to locate the special peak points in normalized interference spectrum and combining the advantages of the

unimodal and bimodal measurement achieves the demodulation of the cavity length. Through online simulation and

actual measurement, the results s how that the peak positioning technology based on BP neural network can not only

achieve high-precision demodulation of the cavity length, but also achieve an absolute measurement of cavity length in

large dynamic range.

Keywords: EFPI Fiber Optical Sensor; The Demodulation of Cavity Length; BP Neural Network; The Peak Pos i tioning

Technology

1. Introduction

EFPI fiber optical sensor is widely used in the gas densi-

ty detecting system with unique advantages, such as small

volume, simple structure and high sensitivity [1]. The

F-P sensor cavity length demodulation is not only a main

way to obtain the information of gas density, but also a

key part of the whole detection system. By the influence

of the light source and the optical wave, traditional de-

modulating mode for the entire demodulation results can

cause great errors. It is difficult to realize stability and

accuracy of signal measurement [2]. There are many me-

thods to demodulate fiber optical sensor cavity length,

such as the intensity demodulation and phase demodula-

tion. Based on previous studies, this paper proposes that

repeated training on the input signal can make the mini-

mized error between the final output value and expecta-

tions, and using the approximation of nonlinear function

achieves the recognition of peak levels.

2. The Basic Principle of EFPI Fiber Optical

Sensing System

The sensor system uses laser as signal source of detecting

gas concentration. The light is emitted by the laser, and it

reaches fiber isolator through optical fiber transmission,

and then light is incident to the F-P cavity when goes

after 2 × 2 couplers. When light combined with gas in the

cavity, interference output signal carrying the informa-

tion of gas density would be transferred by fiber optical

and couplers. The gas density information is demodu-

lated by light interference analyzer, then after photovol-

taic conversion, the clutter signal is filtered off and the

signal is amplified. The signal processing unit analyzes

digital signal transmission, and finally the MCU (Micro

Control Unit) will control signa l ou tpu t and warn prompt.

Fundamental principle of the whole system is shown in

Figure 1.

The advantages of fiber optical EFPI sensor is: high

resolution; high sensitivity; large dynamic range; wide

frequency band; sensing and transmitting large amount of

information; small volume and light weight; corrosion

resistance; electromagnetic interference; easy to reuse the

formation of sensor network; easy real-time, on-line, dis-

Project supported by the National Natural Science Foundation of

China and Shenhua Group Ltd. (Grant No.51174258). Project sup-

ported by the

Natural Science Foundation of Anhui Province, China

(Grant No.11040606M103).

Application of the Spectrum Peak Positioning Technology Based on

BP Neural Network in Demodulation of Cavity Length of EFPI Fiber Optical Sensor

Open Access JCC

Optical fiber transmission

Laser light

source Isolator

Interference

analyzer

Coupler

DMFLock-in amplifier

EFPI sensor

Signal

processing unit

Signal source

Figure 1. The basic principle of EFPI fiber optical sensor

system diagram.

tributed and multiple parameter sensing. Especially EFPI

fiber optical sensor can work in the inflammable, explo-

sive, hig h te mperat ur e and high pressure envi ronments.

3. The Demodulation of EFPI Sensor Cavity

Length by Using the Spectrum Peak

Positioning Technology

3.1. The Basic Principle of the EFPI Sensor

Cavity Length Demodulation

F-P cavity length as shown in Figure 2 is between two

optical polishing surface distances. In order to achieve

the measurement of wide dynamic range and high resolu-

tion, accurate information of the cavity length is obtained

from optical interference signal, which is returned from

the EFPI fiber optical sensor through effective signal de-

modulation. Through tracking changes of wavelengths of

spectral peak in particular interfered order Cavity length

demodulation of EFPI fiber optical sensor which is based

on the spectral peak location will obtain the information

of cavity length. The demodulation method has many

kinds, such as: unimodal measurement, bimodal measure-

ment, BP neural network measurement etc [3]. Though

unimodal measurement resolution is very high, the range

of measurement is finite; bimodal measuring method can

realize the measurement of large dynamic range. How-

ever, the resolution is too low. This paper presents that

using BP neural network locates the spectral interference

spectrum, so that the reso lution of cav ity length wit h wide

dynamic range and high resolution can be achieved. Spec-

tral interferenc e signal s collected by the syste m are treated

to get the change information of long cavity through the

analysis of interference spectrum changes.

3.2. Spectral Peak Location Technology Based

on BP Neural Network

3.2.1. BP Neural Network

BP neural network is a multilayer feed forward network

[4], it mainly consists of three parts: input layer, output

Figure 2. The structure diagram of EFPI fiber optical sen-

sor.

layer and hidden layer. Function f are often used as the

transfer function of neurons to realize arbitrary nonlinear

mapping:

( )

1cx

fx e−

=+,

0c>

(1) [6]

c is the neurons input. Its basic principle is to minimize

the squared error between the expected value and the

output value by adjusting the weights of the network. BP

neural network is divided into forward propagation and

back propagation. In the training process of forward

propagation, each layer of neurons will only change with

a layer of neurons. When the output layer does not reach

the expected value, the actual error is calculated out and

then the error signal fed back to the original. Repeatedly

revising each layer neuron weights makes the error of

prediction to the minimum.

In the whole network, input layer [5] contains N neu-

ron 1

p, 2

p, 3

p,..., n

p, each neuron has a correspond-

ing weight. As shown in Figure 3, 1

p, 2

,..., n

corresponding respectively to weights

,...,

. An offset

is in the hidden layer, all the neurons

and the corresponding weights do multiplication and ac-

cumul a t ion as network input s ignal

tatal

112 2totaln n

pG pGpG

= +++

(2)

If the overall input signal is total

, then

12total n

λ λλλ

=+++

(3)

The input signal of each layer respectively enter the

transfer function f, output signal of neurons

can fi-

nally be obtained through operation processing,

( )

= (4)

3.2.2. The Tracing of Spectral Peak by Using BP

Neural Network

The essence of application of BP neural network spec-

trum peak tracing is to make the correct judgment for

spectral peak of the normalized interference spectrum.

The nonlinear functional approximation of BP neural

network can effectively identify discrete changes of F-P

cavity length in phase space, so that the wavelength val-

Application of the Spectrum Peak Positioning Technology Based on

BP Neural Network in Demodulation of Cavity Length of EFPI Fiber Optical Sensor

Open Access JCC

Figure 3. BP neural network.

ue of the main and secondary maximum peak can be

found out from the normalized interference spectrum that

has been collec ted. After repeated sampling, discrete vari-

ation curve of cavity length in two-dimensional phase

space range is drawn with the main maximum peak wa-

velength values as abscissa and maximum peak wave-

length values as ordinate, as shown in Figure 4.

A three layer BP neural network is constructed for the

change trajectory of cavity length in all phase space.

Taking the main maximum peak wavelength values as

input layer N neurons in input, the output layer corres-

ponds to the maximum peak value of wavelength. The

transfer function f(x) will greatly take peak wavelength

values into operation through repeated training and posi-

tive and negative transmission to correct weight values.

The actual trajectory is compared with the trajectory of

adjacent levels after the training output. The relative er-

ror is shown in Table 1. If the relative error is less than

0.5nm , it shows that accurate position of peaks is suc-

cessfully tracked. We shall assume that using neural

network demodulates interference spectrum with a cavity

length of 1

. Orders of spectral peak k appears at the

point of wavelength 1

1k−

orders show spectral

peak at 2

; When the cavity length change into 2

1k−

orders show spectral peak at the corresponding

wavelength 1

2k−

orders show spectral peak at λ2 +

Δλ, then:

2Lk

= (5)

( )

2 -1Lk

(6)

( )

2 -1Lk

(7)

( )()

2 -2Lk

λλ

=+∆ (8)

Reach: 1

31 1

∆

=++

(9) [7]

After the formula (9) is applied to the formula (5), the

cavity length value 1

L of neural network demodulation

can final l y be obtained.

From the Figure 5, it can be seen that after neural

network demodulation, the cavity length value is very

Figure 4. Phase space trajectory curve of F-P cavity length.

Table 1. Adjacent level maximum peak wavelength and

relative error.

Secondary maximum

peak value Ma in ma xi mum

peak value Relative error

1.30 1.41 0. 11

1.32 1.46 0.14

1.41 1.52 0. 11

1.41 1.54 0.13

1.52 1.58 0.06

1.61 1.62 0.01

1.59 1.63 0.04

1.60 1.64 0.04

1.59 1.67 0.08

1.64 1.75 0. 11

Figure 5. Demodulation of cavity length and actual cavity

length comparison diagram.

close to the actual cavity length value, which shows the

superiority of this demodulation method [8].

50 The cavity length value (um)

100 150200250

100

150

200

250

The demodulation of cavity length value (um)

The demodulation of cavity length

The actual cavity length

Application of the Spectrum Peak Positioning Technology Based on

BP Neural Network in Demodulation of Cavity Length of EFPI Fiber Optical Sensor

Open Access JCC

4. Improved Algorithm of Neural Network

Because BP neural network has the disadvantage of slow

converging speed and a tendency to the local extreme

operation. Serious impact on its generalization ability is

not conducive to the demodulation process of cavity

length. To overcome the disadvantages, it can be respec-

tively from two aspects of sample set and the weights in

improving neural network algorithm. A steepness factor

is introduced in the transfer function

()fx

( )

fx e

−

(10)

An error plane exist flat area [9], which makes the dif-

ference between the network output and the expected

value. After importing the steepness factor δ and making

, the input space of neurons is reduced. When

the input neurons decrease δ times. The growth of neuron

function’s sensitive area leads to the input neurons into

the unsaturated area. When

, the transmission func-

tion

()fx

recovers to its original state, which has high

sensitivity for small input.

From Figure 6, joining the steepness factor can effec-

tively improve the insufficiency of neural network and

the network generalization ability.

Training sample

Output data

(a) Sample input and ou tput

Output data

Training sample

(b) Validation sample input and output

Deviation

Training times

Figure 6. The simulation results of improved algorithm of

neural network diagram.

5. The Results of Experiment and Simulation

Analysis

Spectral peak locating technology based on neural net-

work shows that, for the normalized interference spec-

trums of different SNR (signal-to-noise ratio), there are

obvious differences in capturing error of the starting point,

the vertex point and the end point. The spectral peak lo-

calization can be effectively realized by using NMME

formula:

NMMEmean abs∧−







(11)

Where

is the estimated position of peak, p is the

real position of peak and N is the sampled data points of

the discrete Fourier transform.

The simulation in Figures 7 and 8 shows that when

SNR is greater than 5 dB, the estimated peak value

NMME will below 6%. In the same SNR, using neural

network to locate peaks of normalized error is signifi-

cantly less than the unimodal or bimodal measurement.

Normalized error

Neural work method

Unimodal (bimodal) measurement method

SNR (dB)

Figure 7. The normalized error of spectrum peak starting

point under different signal to noise ratio.

Normalized error

Neural work method

Unimodal (bimodal) measurement method

SNR (dB)

Figure 8. The normalized error of spectrum peak end point

under different signal to noise ratio.

Application of the Spectrum Peak Positioning Technology Based on

BP Neural Network in Demodulation of Cavity Length of EFPI Fiber Optical Sensor

Open Access JCC

6. Conclusion

Whether in theory or in practice, peak tracking technique

based on BP neural network can realize the demodulation

of F-P cavity length information and solve the defect of

the single (double) peak measurement method which can

not realize the measurement of high resolution, high dy-

namic range [10]. By introducing the factor of gradient to

improve the neural network algorithm, the cavity length

demodul a t ion accura c y is stre ngthene d.

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