RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES1001, doi:10.2205/2007ES000278, 2008
[10] The DMA-based algorithms DRAS and FLARS [Gvishiani et al., 2003, 2004] are an alternative approach (with respect to the methods presented in section 2) to modeling of human reasoning and actions in search for anomalies. DRAS and FLARS are an attempt to model the logic of a researcher recognizing an anomaly from visual inspection of a record for an automated use of this model in analysis of large sets of data that cannot be manually processed. These algorithms yield estimates for boundaries of sought anomalies and subdivide them morphologically into initial, central, and final stages, identifying strong and weak phases in the central stage [Gvishiani et al., 2003]. The algorithms are rather versatile due to a wide set of "rectifications'' [Gvishiani et al., 2003, 2004] arising in modeling interpreter's work.
[11] In a simplified form, work of an interpreter detecting an anomaly by visual inspection of a record is understood here as follows. Initially he looks over the record, estimating activity of its fragments in terms of positive numbers and mentally assigns the inferred numerical estimates to the fragments or their centers. Thus, the interpreter passes from the initial record to a nonnegative function that can be naturally called "rectification'' of a record. Actually, larger values of this function (rectification) will correspond to record points that are more active from the standpoint of sought signals. Further, the interpreter searches for rises in the record rectification that correspond to the most active record fragments. Thus, the interpreter works at two levels, local (rectification of a record) and global (search for rises in the rectification).
[12] Naturally, the proposed simplified model of interpreter's logic cannot be regarded as unique and/or universal. Moreover, interpreter's reasoning is largely determined by the concrete type of anomalies (data) in question. However, in our opinion, the rectification process functions, one way or other, in any case.
[14] Let a discrete positive semiaxis be
and let
y = {yk = y(kh)} be a finite time series (FTS) defined in the interval
(recording period)
We introduce a local survey parameter
D > 0 multiple of
and define a local survey fragment of the record
y with a center at
kh
T as the interval
![]() |
[16] A rectification determination can be regarded as successful if anomalies identified by an interpreter are mapped onto rises in the rectification. Accordingly, the presence of training data (i.e. results obtained by an interpreter from processing of a sufficiently long record fragment) is beneficial to the construction of a rectification. Examples of rectifications:
(1) survey fragment length,
![]() |
(2) survey fragment energy,
![]() |
![]() |
[17] Many other types of rectification were used in [Gvishiani et al., 2003, 2004; Zlotnicki et al., 2005]. At a local level common to algorithms of the DRAS and FLARS families, the rectification Fy is constructed and specified for a record y. This transformation of a record is the first stage of visual analysis performed by an interpreter.
![]() |
Figure 1 |
[20] To implement this procedure, the algorithm uses one-side measures
LaFy(k) and
RaFy(k) that quantify, on the [0, 1] scale, the quietness of the rectification
Fy left and right of the point
kh, detecting points whose ordinates exceed a level
a [Gvishiani et al., 2003].
The latter is a free parameter of the
algorithm called the vertical level of background. In other words, the quietness
to the left (right) of the point
kh in the record
y is modeled in DRAS as a
fuzzy subset on the recording interval
T with the measures
LaFy(k) (RaFy(k)). Using the conjunction
min(LaFy(k), RaFy(k)),
provides for the possibility of versatile treatment of
Fy excesses over the level
a. With the so-called horizontal level
b[0, 1] being properly adjusted, DRAS extracts only sufficiently dense (in time)
excesses and takes no account of insignificant fragments considering them as
background. This is attained by dividing the recording interval
T into
background (quiet) and potentially anomalous (disturbed) parts:
[21] The set
P is the union of the connected components
It is these
components that are processed by DRAS at the second stage of the global level.
Identification of significantly anomalous intervals
An in
Pn is based on
monitoring of the difference
DaFy(k) = LaFy(k) - RaFy(k),
which is reflected in the name of the algorithm (difference recognition algorithm for signals).
The beginning of the anomaly
An coincides with the first maximum of
DaFy(k) in
Pn.
Actually, the difference between the quiet level to the left and the disturbed
level to the right is most pronounced for the first time precisely at this
point. For the same reason, the end of the anomaly
An coincides in time with
the last negative minimum of
DaFy(k) in
Pn. This procedure of identification of
anomalies
An is described in detail in
[Gvishiani et al., 2003].
[22] Free parameters of DRAS are the rectifying functional
F and the following
positive values: the local survey window
D |T|, the vertical level of
background
a, the global survey window
L > D, and the
horizontal level of background
b
[0.5, 1]. Accordingly,
the algorithm can also be written as DRAS
(F, D, a, L, b).
[24] We remind the reader that the DRAS choice of extreme points is based on analysis
of the vertical level
a immediately in the rectification
Fy. FLARS
forms indirectly the set of anomalous points
A, using the search for extreme
values on a
Fy topography with the help of a fuzzy extremality measure
m(k) taking values from the interval
-1 m(k)
1 [Gvishiani et al., 2004].
The measure is constructed on
Fy on the basis of fuzzy comparisons
(5) and the vertical extremality level
t
[-1, 1]. The
T interval is
divided into a set of significantly anomalous points
A and its complement
![]() |
Like DRAS, the FLARS algorithm divides the set of nonanomalous points is
subdivided into background and potentially anomalous components with the help of
the alternating one-sided measures
and
and the horizontal background level
![]() |
Note that, due to the normalization
m(k) [-1, 1], the FLARS choice of the extremality level
t is somewhat simpler compared to DRAS:
t is usually set equal to 0,
0.5, or 0.75. A detailed description of FLARS is given in
[Gvishiani et al., 2004].
[25] Free parameters of FLARS are the rectifying functional
F and the following
positive values: the local survey window
D |T|, global survey window
L > D, and vertical level of extremality
t. Accordingly, the
algorithm can be designated as FLARS
(F, D, L, t).
Citation: 2008), Recognition of anomalies from time series by fuzzy logic methods, Russ. J. Earth Sci., 10, ES1001, doi:10.2205/2007ES000278.
Copyright 2008 by the Russian Journal of Earth Sciences (Powered by TeXWeb (Win32, v.2.0).