Copyright © 2015 IJEIR, All right reserved
681
International Journal of Engineering Innovation & Research
Volume 4, Issue 5, ISSN: 2277 – 5668
Data Mining Algorithm for Off-Group Points on Noise
Polluted Time Series Based on ESO
Fuxin WANG
Engineering Research Center on Shipping
Simulation by the Ministry of Education,
Shanghai Maritime University, Shanghai
201306, China
Zhijian HUANG*
Engineering Research Center on Shipping
Simulation by the Ministry of Education,
Shanghai Maritime University, Shanghai
201306, China
Email: zjhuang@shmtu.edu.cn
Yanyan ZHANG
Central Lab of the 10th affiliated people’s
hospital, Tongji University, Shanghai
200072, China
Liang QIAO
Engineering Research Center on Shipping Simulation by the
Ministry of Education, Shanghai Maritime University,
Shanghai 201306, China
Pinyou LI
Engineering Research Center on Shipping Simulation by the
Ministry of Education, Shanghai Maritime University,
Shanghai 201306, China
Abstract – The practically measured signals always contain
wild values deviating far from true values. How to remove
these wild values is an important research project for data
mining of off-group points. In active disturbance rejection
controller (ADRC), it is difficult to acquire accurate signal,
since the signal is vulnerable to the influence of the wild
values. Therefore, this paper puts forward extend state
observer (ESO) algorithm to replace tracking differentiator
(TD) method. The performances are compared between them
under equal conditions and for different rang of wild values.
The result suggests that the ESO algorithm will remove the
wild values effectively and better, when it’s relatively small.
Keywords – ADRC, TD, ESO, Remove Wild Values, Data
Mining.
1
I. INTRODUCTION
It is an inevitable problem that wild values exist in
signals. So related algorithms on the elimination of wild
values are extensively applied to many fields, such as
image processing. In recent years, more and more experts
begin to pay attention to mining algorithm[1-5] similar to
the elimination of wild values. Mining algorithm can avoid
the difficulties of analyses resulted from detailed
consideration of the consumption of energy. Now we
present extend state observer (ESO) algorithm to the
elimination of wild values.
Signals with high precision, small fluctuation and better
effect will be acquired if wild values existed in the signals
are eliminated. Therefore, there are many research
methods of the elimination of wild values. Some experts
raises the method of restoring signals to eliminate wild
values by improving damage identification techniques of
signals[6], and then applying advanced techniques to
restoring signals. But this approach is too idealized and
has large technique barriers. Some experts suggest the
segmentation of signals[7], that is to say, dividing the
signal processing flow into several phases, processing
respectively, and finally combining the unified USB of
procedures. But this method is too complicated to apply to
the practice. Other experts use Tracking Differentiator
This work was supported by the NSFC Projects of China under
Grant No. 61403250.
(TD) to extract differential signals and arrange the process
of transition, since TD can be more accessible to extract
differential signals and remove wild values at the same
time[8-9]. But using TD to remove wild values will lead to
high losses of phases and distortion, so sometimes
accurate signals can not be acquired.
On the basis of analyzing the previous related researches
and deeply studying Extend State Observer (ESO)
algorithm[10-13], we raises a new method to eliminate
wild values, that is, by using ESO to remove wild values
existed in signals. This method relies less on the system,
and removes wild values to the most extent, so that the
most accurate signals can be acquired.
II. THE ESO ALGORITHM
The ESO is the key part of the active disturbance
rejection controller active disturbance rejection controller
(ADRC)[14], by observing external variables to determine
state variables inside the system, expanding disturbing
actions able to affect controlled output into new state
variables and using special feedback system to observe the
extend state. Actually, The ESO is a linear differential
equation, whose principle is as follows:
For a given second-order linear control system
12
2 1 1 2 2
1
xx
x a x a x bu
yx
(1)
The form of ESO corresponding to this linear system is
11
1 2 1 1
2 1 1 2 2 2 1
e z y
z z l e
z a z a z l e bu
(2)
As regard to non-linear control system, let
12
2 1 2
1
xx
x f x x bu
yx
(3)
When the function
and b are known, then the
form of ESO is