http://www.paper.edu.cn
Application of improved Grey prediction model for settlement prediction
of roadbed
①
XIE Zheng-wen (谢正文)，HU Han-hua （胡汉华），LI Ming(李明)
(School of Resources and safety Engineering, Central South University, Changsha 410083, China)
Abstract
An improved Grey-based settlement predictor is promoted. Adopt Grey prediction as a forecasting means because of its
fast calculation with a few of data inputs needed. However, our preliminary study shows that the general Grey model,
GM (1, 1) is inadequate to handle settlement prediction as its only adapt to the data with exponential law. And the defect
was the coefficient’s choice of α and
in prediction formula. In this study, the prediction is improved significantly
by applying the transformed Grey model and the concept of average system slope. The adaptive value of α in the Grey
differential equation is obtained quickly with the average system slope technique. The example show that the prediction
accuracy has been improved quite a lot in comparison with general grey model.
(1)
ˆ
(1)X
Keywords: Grey theory; Average slope; Settlement prediction; Roadbed
CLC number: TU433 Document code: A
1. Introduction
Settlement and stability are two primary considerations systematically related to the design of an embankment on soft ground the tools
available for stability evaluation seem to be satisfactory. The key element of long term behavior of the embankment routinely subjected to
design analysis is the settlement
[1]
. In other words, the settlement analysis is the most appropriate approach to the embankment analysis.
Many researchers developed the settlement prediction methods, ‘Three Point Method’,’ Hyperbola Method’, ‘Grey Theory’
[2]
,’ Neural
Network’
[3]
,’Asaokao’
[4]
etc. Grey theory is one of the most widely used methods. Grey theory, developed originally by Deng
[5]
, is a truly
multidisciplinary and generic theory that deals with systems that are characterized by poor information and/or for which information is
lacking. The fields covered by grey theory include systems analysis, data processing, modeling, prediction, decision making and control.
Grey forecasting models have been extensively used in many applications
[6-9]
, and it was improved by many researchers.
The advantages of the proposed improved Grey-based settlement predictor are its fast calculation and ease of implementation with a few
data inputs required. And it has satisfactory fitting effects and thus points a novel direction to higher modeling precision.
2. General Grey predictor
2.1. GM (1, 1) model
Deng proposed Grey theory to deal with indeterminate and incomplete systems
[10]
. Unlike conventional stochastic forecasting theory,
Grey theory simply needs few sample data inputs to construct a Grey model. Since the poor regularity for the tested settlement data, the
AGO technique in Grey forecasting is suitable to reduce the randomization of the raw data efficiently. Generally, the procedure for GM (1, 1)
forecasting is explained as follows:
Step 1.Denote the original data sequence by
(0) (0) (0) (0)
{(1), (2),, ()XXX Xn=⋅⋅⋅}
(1)
Where n is the number of data observed.
Step 2.The AGO formation of
(0)
x
is defined as:
(1) (1) (1) (1)
{(1), (2),, ()XXX Xn=⋅⋅⋅}
(2)
Where
(1) (0)
(1) (1)XX=
and
(1) (0 )
1
() { (), 1,2,3 ,}
k
i
X
kXik
=
n
=
=⋅⋅⋅
∑
(3)
The GM (1, 1) model can be constructed by establishing a first order differential equation for as:
(1)
X()k
①
Foundation item: project (ZCK001-04) supported by the foundation of Zhucheng road.
Biography: Xie Zhengwen (1981- ), male, master student,
xiezhengwen114@163.com.
1
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