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
67
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.
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
68
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:
( )
1
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 p,
3
p
,..., n
p
corresponding respectively to weights
1
G
,
2
G
,
3
G
,...,
n
G
. An offset
a
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
λ
:
112 2totaln n
pG pGpG λ = +++
(2)
If the overall input signal is total λ , then
12total n
λ λλλ =+++
(3)
The input signal of each layer respectively enter the
transfer function f, output signal of neurons
κ
can fi-
nally be obtained through operation processing,
( )
Kf ω = (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
69
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
L
. Orders of spectral peak k appears at the
point of wavelength 1
λ
,
1k−
orders show spectral
peak at 2
λ
; When the cavity length change into 2
L
,
1k−
orders show spectral peak at the corresponding
wavelength 1
λ
,
2k−
orders show spectral peak at λ2 +
Δλ, then:
11
2Lk
λ = (5)
( )
12
2 -1Lk λ =
(6)
( )
21
2 -1Lk λ
=
(7)
( )()
22
2 -2Lk
λλ
=+∆ (8)
Reach: 1
4
31 1
22
k
λ
λ ∆
=++
(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
50
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
70
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
δ
is introduced in the transfer function
()fx
:
( )
/
1
1
cx
fx e
δ −
=+
(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
1 δ >
, the input space of neurons is reduced. When
1 δ >
,
the input neurons decrease δ times. The growth of neuron
function’s sensitive area leads to the input neurons into
the unsaturated area. When
1 δ =
, 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
(c) Training times and error
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:
pp
N
NMMEmean abs∧−


=




(11)
Where
ˆ
p
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
71
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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