a quantitative method for dynamic risk prediction …...a quantitative method for dynamic risk...

International Journal of Safety Science

Vol. 01, No. 03, (2017), pp. 61-73

DOI:10.24900/ijss/01036173.2017.1201

61

A Quantitative Method for Dynamic Risk Prediction Using AHP

and Grey Modeling: Case Study of a Mud-Flow Hazard

Li-Jeng, Huang1 *

1

1Department of Civil Engineering, National Kaohsiung University of Applied Sciences,

Kaohsiung 807, Taiwan, R.O.C

Abstract

A quantitative technique for dynamic risk assessment of mud-flow hazards using the

integrated skills of analytical hierarchy process (AHP) and grey modelling theory (GM)

is developed and verified with a real case occurred in Taiwan. Theoretical model of AHP

is first built for risk assessment of mud-flow hazards in which 9 important influence

factors considering topological, metrological and rain-fall conditions are selected and

their relative risk impacts are analyzed. Among these 9 influence factors the GM(1,1)

models are employed for intensity of rainfall and accumulated rainfall while linear model

is employed for duration of rainfall for prediction. Two predicted schemes are proposed:

(1) Single-step prediction (SSP) scheme, and (2) Recycling point-wise prediction (RPP)

scheme. The real case of mud-flow disasters occurred in Taiwan is tested by the use of

AHP/GM: the mud-flow occurred in Tung-Shing village, Hua-lien, July 10-11, 1994. The

results show that the proposed AHP/GM integrated quantitative dynamic risk assessment

schemes can provide early precaution, warning and alarming in time for the occurrence

of mud flow disaster. Using appropriate grey modeling for dynamic influence factors as

well as AHP framework and criteria can successfully predict the risk change of mud-flow

hazards.

Keywords: Mud-flow; Analytical Hierarchy Process (AHP); Grey Modeling (GM);

Grey Prediction; Dynamic Risk Assessment

Nomenclature

][B comparison matrix of influence factors in criteria layer

][C comparison matrix of influence factors in sub-criteria layer

]ˆ[C state-to-output transformation matrix containing relative risk impact (RRI)

}{E judgment vector of evaluated values of influence factors

ORI overall risk index

}{RRI relative risk impacts

)()0( kx whitening original set in grey modelling

)()1( kx accumulated sequences in grey modelling

)(~ )0( kx predicted sequences in grey modelling

)(~ )1( kx predicted accumulated sequences in grey modelling

)}(ˆ{ tx state vector describing the time-varying judgment vector

)}(ˆ{ ty output vector of the predicted overall risk indices.

1 * Corresponding author. Tel.: +0-886-73437841; fax: +0-886-73478019

E-mail address: [email protected]


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)()1( kz mean sequences in grey modelling

1. Introduction

Recently risk assessment of debris-flows becomes an important research topic and

many research works were conducted wherein various methods were proposed such as

empirical methods (Jacob, et al. 2012) [1]; (Cui, et al. 2013) [2], probabilistic methods

(Arkset, et al. 2007; Hu, et al. (2008); Xu, et al (2013)) [3-5]; GIS (Wang, et al. 2011) [6];

multi-mode analysis (Tian, et al., 2011) [7]; fuzzy reasoning (Lin, et al. 2012) [8], 3-steps

approach (Settimo, et al. 2016) [9]; etc. However, a real-time quantitative method is

necessary for practical implementation of precaution and warning system for debris-flows

in order to rescue human beings and property.

Occurrence of debris flow depends highly on local topographic, meteorologic, geologic,

and hydrologic conditions (Takahashi, 1991) [10]. Many disasters caused by stony and

mud flows in Taiwan were reported and studied (Jan and Shen, 1993; Wu, et al. 2006; Lin,

2006) [11-13]. The special reasons that Taiwan is prone to debris-flow hazards have also

been reported (Jan, 2000; Huang, 2001)[14-15]. Debris flows are inherently dynamically

developing temporarily and/or spatially (Peng, 2015) [16].

In Taiwan, scientists and engineers also continuously search for appropriate methods

and systems for precaution, warning and alarming of the occurrence of debris flows.

Huang (2014) [17] has reviewed the research work on debris flow mechanisms and the

risk assessment studies in the past in Taiwan. Among these studies some of techniques

based on artificial intelligence have been proposed such as application of probability

theory (Chen and Jan, 2000) [18], intelligent control theory (Chang and Lee, 1997) [19],

expert systems (Lin, 2000) [20], grey relation analysis (Wu, 2002) [21], fuzzy reasoning

system (Chen (2006) [22] and case-based system (Tsai, 2007) [23]. However, most of

these assessment techniques consider only a few influence factors and may be not suitable

for correct prediction debris-flow hazards including multiple influence factors.

Risk assessment task is a multi-level and multi-criteria complicated process. In the

field of operational research, Saaty, T. L. (1980) [24] had proposed the so-called Analytic

Hierarchy Process (AHP) for multiple criteria decision making problems. It is also a good

approach for risk assessment of problem with multi-criteria on influence factors. The

author also had attempted applied AHP to risk assessment of debris-flow hazards

occurred in Sen-Mu and Hua-San (Huang, 2014) [25] and Tung-Men and Tung-Shing

(Huang, et al. 2015) [26], respectively, and the results are verified to be useful.

Since 1982 Deng proposed the concept of grey system for analysis (Deng,1989) [27],

researches and applications of grey system theory to forecasting and prediction of power

load (Tamura, et al. 1992) [28], fault detection (Luo, 1995) [29], earthquake (Jeng and

Chang, 1998) [30], control system design (Wong and Chen, 1998) [31], structure failure

(Liu, et al. 2001) [32] and many examples (Liu et al., 25) [33] have been conducted

successfully.

In this paper an integrated AHP and grey models, namely AHP/GM, is proposed for

building up a quantitative method for dynamic risk assessment and prediction of mud

flow hazards. Three layers and nine influence factors (criteria) are involved in the

structure of AHP. The relative judgment among each influence factor is built up based

upon 9 scaling levels to form the reciprocal judgment matrices for evaluating weighting

vectors for each layer. After the relative risk impact of each influence factor is obtained,

grey models of GM(1,1) are employed for dynamic prediction of intensity of rainfall and

accumulated rainfall, while linear model is for the duration of rainfall, after a selected


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base point. And finally the time-varying overall risk index can be obtained. Two schemes

of prediction are proposed and tested, one is the Single-Step Prediction (SSP) and the

other is the Recycling Point-wise Prediction (RPP). The proposed AHP/GM methods will

be applied and verified using a practical case of disasters occurred in Tung-Shing Village

of Hua-Lian County in eastern Taiwan.

2. Framework of Dynamic Risk Assessment

The framework of dynamic risk assessment for a problem using integrated AHP

and grey modelling (GM) technique can be illustrated in Fig. 1. In the process, AHP

technique is employed to analyze the relative risk impacts (RRI) from the

comparison matrices of the multiple influence factors in hierarchical structure

(obtained from questionnaire method), and grey modelling scheme is adopted for

dynamic prediction of time-varying evaluated values corresponding to influence

factors (some time-invariant values are kept constant), and finally the time-varying

overall risk index (ORI) can be calculated and employed as dynamic risk assessed

results for precaution and warning of occurrence of disasters.

Fig. 1 Framework of dynamic risk assessment using integrated AHP and grey modelling technique.

In the following a typical model and process of dynamic risk assessment using

integrated AHP and grey modelling technique will be built and explained

considering the case of debris/mud flow hazard.

3. Relative Risk Indices Obtained Using AHP Model

The procedures to construct AHP model for risk assessment of mud flow hazards

and to obtain relative risk indices had been studied by Huang (2014) [25], Huang, et

al. (2015)[26]. The basic procedures are as follows:

(1) Establish a hierarchical model

(2) Setup comparison matrices

(3) Calculate the relative weights and the maximal eigen-values

(4) Check the consistency

(5) Evaluate the final assessed risk index

The top of a hierarchical model is the goal to be achieved by AHP, shown in Fig.

2. The second layer (criteria layer) refers to the proposed major categories of

influence factors. Factors in the third layer (sub-criteria-layer) support the factors in

the second layer.

Risk assessment

problems

(multiple

influence

factors)

AHP

Relative

Risk

Impacts

][]ˆ[ RRIC

Time-Invariant evaluated value of

influence factors {E}

Time-varying evaluated value of influence

factors

{E(t)}

Grey system

theory: GM(1,1)

)}({ 0 tx

Predicted overall risk

index

)}(ˆ]{ˆ[

)(ˆ)(

txC

tytORI


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Fig. 2 Hierarchical model of the risk assessment of debris/mud flows hazards using AHP

Comparison matrices are obtained through filling in a questionnaire form by some

experts in this field. Here we adopt 1-9 scaling method as suggested by Saaty (1980)

[24] . The following judgment matrices are built up:

44

1

33 12/12/14/1

213/23/1

22/312/1

4321

][

142

4/112/1

2/121

][

x

CB

3312/33

3/212

3/12/11

]3[

2213/1

31]2[

x

CC

(1)

The calculated results of the relative risk impact (RRI) of each influence factors

on the overall risk are (Fig. 3):

2857.0

1905.0

0952.0

0357.0

1071.0

0308.0

0503.0

0682.0

1364.0

5714.0

1429.0

2857.0

5.000

3333.000

1667.000

025.00

075.00

001078.0

001761.0

002387.0

004774.0

}{RRI (2)

C21. Effective Area of Watershed (EA)

C22. Out-Flow of Sediment (OS)

C14.

Surface Plants (SP)

AHP Model for Risk Assessment of Debris/Mud Flow Hazards

B1.

Topological & Geological Conditions (TG)

B2.

Watershed Conditions (WS)

B3.

Rainfall Conditions (RF)

C12. Type of Deposit (TD)

C13.

Grain Size Distribution (SD)

C11. Averaged Slope Angle (SA)

C31. Intensity of Rainfall (IR)

C32. Duration of Rainfall (DR)

C33.

Accumulated Rainfall (AR)

Goal Layer

Risk Factors Layer

Risk Factors Sub-Layer


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Fig. 3 Diagram for relative risk impact (RRI) for influence factors of mud-flow hazards using AHP

1. Dynamic Risk Assessment and Prediction Based on GM(1, 1) Model

1.1. Build up the evaluation criteria for each influence factor

The evaluation value and criteria for mud-flow occurred in Taiwan is proposed as

reported in Huang (2014) [25], Huang, et al. (2015) [26]. The criteria depend on

special real situations for different countries.

1.2. Identify static and dynamic risk influence factors

In the AHP model we can find that 6 influence factors 221211 ,, CCC are nearly

static and not vary with time significantly and we can consider these are static

variables; while 3 influence factors 3231, CC and 33C are inherently time-dependent.

The mapping relationship between the quantities of dynamic influence factors and

judgment vector components can be expressed as follows:

(1) Intensity of rainfall (I) and E7 (C31):

hrmmTfor

hrmmThrmmforI

hrmmIfor

CE

/20,9

/20/5),5(520

191

/5,1

)( 317

(3)

(2) Duration (T) and E8 (C32):

hrTfor

hrThrforT

hrTfor

CE

20,9

201),1(120

191

1,1

)( 328 (4)

(3) Accumulated rainfall (A) and E9(C33):

mmAfor

mmAmmforA

mmAfor

CE

400,9

400100),100(100400

191

100,1

)( 339

(5)


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1.3. Build up the prediction models

(1) Linear Model:

Assuming we have original data set )(,),2(),1( )0()0()0(atxxx which is linearly

varying such as the duration of rainfall (C32) in AHP of mud flow hazards, then the

predicted sequences can be directly obtained as

Paaa Nptpmtxptx ,,2,1),()()( )0()0( (6)

where at is the time for activating prediction, pN is the total number of points to

be predicted; m is the linear slope of the line between 1t to att .

(2) GM(1,1)-based Exponential Growth Model:

When the original data set )(,),2(),1( )0()0()0(atxxx vary in a time-growing type,

such as the intensity of rainfall (C31) and the accumulated rainfall (C33) in AHP of

mud flow hazards, the GM(1,1) model can be employed for grey modeling and grey

prediction. The basic procedures can be summarized as follows:

(1) Obtain }{ )1(x from }{ )0(x using accumulated generating operation (AGO):

)()( )0(

1

)1( mxkxk

m

(7)

(2) Obtain the mean sequences }{ )1(z :

atkkxkxkz ,,3,2,2/))1()(()( )1()1()1(

(8)

(3) Calculate the matrix ][B and vector }{Y :

)(

)3(

)2(

}{,

1)(

1)3(

1)2(

][

)0(

)0(

)0(

)1(

)1(

)1(

aa tx

x

x

Y

tz

z

z

B

(9)

(4) Calculate the parameter vector:

}{][])[]([ 1 YBBBb

a TT

(10)

(5) Build up the GM(1,1) model for }{ )1(x :

a

be

a

bxkx ka )1()0()1( ))1(()(~ (11)

(6) Obtain the whitening original set:

)1(~)(~)(~ )1()1()0( kxkxkx (12)


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(7) Evaluate the predicted sequence )(~ )0( ptx a :

(7a) Single-Step Prediction (SSP) Scheme: when this scheme is employed, the

original data }{ )0(x is employed for building the GM(1,1) model and the predicted

sequences are obtained at a time:

Ppta

a Npa

be

a

bxptx a ,,2,1,,))1(()(~ )1()0()1(

(13)

Paaa Npptxptxptx ,,2,1,),1(~)(~)(~ )1()1()0( (14)

(7b) Recycling Point-wise Prediction (RPP) Scheme: when this scheme is

employed, initially we use the first aN~1 points to build GM(1,1) model and predict

only single point for )1(~ )1( atx and )1(~ )0( atx ; and in the 2nd cycle we use 1~2 aN

original data set to to build GM(1,1) model and predict only single point for

)2(~ )1( atx and )2(~ )0( atx , and continuously recycling the process to obtained all the

predicted sequence pa Npptx ,,2,1),(~ )0( .

amta

a tma

be

a

bmxmtx a ,,2,1,,))(()(~ )1()0()1(

(15)

aaaa tmmtxmtxmtx ,,2,1,),1(~)(~)(~ )1()1()0( (16)

Since in each step one data point (old information) is updated and replaced by the

newest data (new information) and this scheme is expected to be more precise than

the SSP.

1.4. Evaluate the final dynamic overall risk index

From the previous study on the risk assessment of mud flow hazards using AHP

model [25, 26], the overall risk index can be evaluated as

iii

T ERRIERRIORI

9

1}{}{ (1

7)

where }{E is a 19 vector denoting the evaluation value of each influence factor

(sub-criteria). We can extend this to dynamic assessment situation and write the

equation in alternate form:

)}(ˆ{]ˆ[)()}({)}(ˆ{9

1

txCtERRItORIty iii

(18)

where )}(ˆ{ ty denotes the output vector of the predicted Overall Risk Index (ORI),

]ˆ[C is the state-to-output transformation matrix containing the Relative Risk Impact

(RRI), and )}(ˆ{ tx denotes the state vector describing the time variation of judgment

vector


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2. Application of AHP/GM Quantitative Method to Dynamic Risk Assessment of Mud-Flow Hazards

2.1. Description of mud-flow disasters occurred in Tung-Shing village in eastern Taiwan

The case of mud-flow disaster we employed for checking the validity of risk

assessment model is a mudslide occurred at July 10-11, 1994, in the Tung-Shing

Village, Fung-Bin township, Hua-Lien County, Taiwan during the attack of

Typhoon with strong storms (Fig. 4). This mud-flow caused more than 50 deaths.

Chang (1995) [34], Chen and Shieh (1996) [35], had reported the mud flow caused

disasters.

Fig. 4 Location of two cases of mud-flow hazards occurred in Eastern Taiwan

2.2. Recorded data and judgment vector {E}

(1) Static data of mud flow occurred in Tung-Shing Village

The judgment vector components for those static data ),,,( 621 EEE corresponding

to the influence factors ),,,( 221211 CCC are list in Table 1.

Table 1. Recorded data of investigation of mud-flow hazards occurred at Tung-Shing village

A. Risk assessment of mud-flow hazards Recorded data Rank

(1-9)

B1. Topological & geological conditions

C11. Average Slope Angle(θ ) (Degree) Source area (16~17o)

Truck (12~16o) Deposit (6o)

5

C12. Type of Deposit Crashed rocks 7 C13. Grain Size Distribution Fine grained content:

(1) upstream: 30%

(2) mid-region: 45% (3) downstream: 65%

7

C14. Surface Plants Shallow rooted trees 7

B2. Watershed conditions C21. Effective Area of Watershed (m2) 660000 m2 9

C22. Out-Flow of Sediment (m3) 122000 m3 9

(2) Dynamic data of mud flow occurred in Tung-Shing village

Figure 5(a) shows the real record for the intensity of rainfall at Tung-Shing

Rainfall Measurement Station from 1:00 a.m., July 10, 1994 to 3:00 a.m., July 11,

1994, i.e., totally 27 hours (Chen, et al. 1996) [35]. And the duration and

accumulated rainfall are expressed in Fig. 5(c) and Fig. 5(e), respectively. Based on

21.5

22

22.5

23

23.5

24

24.5

25

25.5

119.5 120 120.5 121 121.5 122 122.5

Taiwan Map

Tung-Shing,Hua-

lien, July

10-11, 1994


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the AHP model the judgment vector components )(),( 87 tEtE and )(9 tE corresponding

to the influence factors ),,( 333231 CCC are shown in Fig. 5(b), 5(d) and 5(f),

respectively. It can be observed that intensity of rainfall varies significantly.

Fig. 5 Original data of intensity of rainfall, duration and accumulated rainfall at Tung-Shing village

and the associated judgment vector components )(),( 328317 CECE , and )( 339 CE before disaster

occurrence

2.3. Dynamic risk assessment of mud-flow hazard occurred in Tung-Shing village

We choose the data points from 1 to 15 for analysis )15( aN and then predict the

data from 16 to 27 )12( PN . The real temporal point of mud flow disaster is at the

point between 23 and 24 (23:30 p.m., July 10, 1994). We expect to have earlier

precaution of the hazard before the occurrence and thus to get more time for

warning, alarming and preparation of rescuing people. For practical implementation

of alarming system, we assume to set the warning time at 6ORI and the alarming

time at 7ORI . (It can be adjusted depending on practical requirement).

(1) Single-Step Prediction (SSP) Scheme:

Using this scheme only a single cycle grey modeling and prediction is conducted.

Using the first 15 data of intensity of rainfall and accumulated rainfall to build

GM(1,1) models to obtain the whitening data pa NNkkx ,2,1),(ˆ )1( and the

predicted original data set pa NNkkx ,2,1),(ˆ )0( using Eq. (7~13); while the

duration of rainfall is predicted using linear law, Eq. (6). The dotted lines in Figure

6(a), 6(c), and 6(e) are predicted using SSP schemes; while the corresponding

judgment vector components )(ˆ),(ˆ87 tEtE , and )(ˆ

9 tE are shown in Fig. 6(b), 6(d) and

6(f), respectively. It can be observed that the predicted intensity of rainfall and

accumulated rainfall, as expected, grow exponentially with time. Figure 7 shows the

final ORI prediction using SSP scheme in which the predicted curve is much

deviated from the real one. However, using this SSP scheme we can have early

precaution of the mud flow disaster (warning before 7 hours and alarming before 5

hours).


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Fig. 6 SSP predicted results of intensity of rainfall, duration and accumulated rainfall at Tung-

Shing village and the associated judgment vector components )(),( 328317 CECE , and )( 339 CE before

disaster occurrence

Fig. 7 SSP predicted results of overall risk index (ORI) at Tung-Shing village

(2) Recycling Point-wise Prediction (RPP) Scheme (Rolling Prediction Scheme):

It can be observed that due to the final points of data set in each cycle for GM(1,1)

analysis are updated by the new coming real data, the predicted results (dashed lines)

for intensity of rainfall (Fig. 8(a)), accumulated rainfall (Fig.8(e)) and their

corresponding judgment vector components (Fig. 8(b) and Fig. 8(f)) are closer to the

real results as compared with those in Fig. 10 using SSP. The resul ts are reasonable

because only single data point is predicted in each cycle and always the newest data

are employed for building the grey modelling. Furthermore, Figure 9 shows the final

ORI prediction using RPP scheme in which the predicted curve is also closer to the

real one than that in Fig. 7. However, we should notice that even it is more precise

in the predicted time of occurrence but the time of earlier precaution would be

sacrificed (warning before 5 hours and alarming before 1 hours).


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Fig. 8 RPP predicted results of intensity of rainfall, duration and accumulated rainfall at Tung-

Shing village and the associated judgment vector components )(),( 328317 CECE , and )( 339 CE before

disaster occurrence

Fig. 9 RPP predicted results of overall risk index (ORI) at Tung-Shing village

3. Conclusion

Correct quantitative techniques for risk assessment and prediction are required for

precaution, warning and mitigation of various kinds of disasters. An effective and

efficient AHP/GM-based quantitative approach for dynamic risk assessment and

prediction of mud-flow hazards is presented and successfully verified using a

practical recorded data of mud-flow disaster occurred in Tung-Shing Village,

Taiwan. In this approach, AHP is employed for building the hierarchical structure of

influence factors and evaluate the relative risk impacts (RRI) of influence factors;

whereas the GM(1,1) models are employed for grey modelling the dynamic variation

of intensity of rainfall as well as accumulated rainfall for dynamic risk prediction.

Single-Step Prediction (SSP) scheme and Recycling Point-wise Prediction (RPP)

scheme are proposed and compared with each other. Important findings are:

(1) Integrated AHP and GM theory to build up an AHP/GM-based quantitative

dynamic risk assessment and prediction method is for mud flow hazards including


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multiple influence factors is feasible. With this method the major influence factors

can be constructed and ranked, the relative risk impact of each influence factors can

be evaluated, and the overall risk index of mud-flow hazard can be obtained

including static influence factors and dynamic ones which are predicted using

GM(1,1) models.

(2) SSP scheme provides a single cycle and convenient approach for dynamic risk

prediction. In general long-term predicted results might deviate from the real values

too much and thus over-estimate the risk potential. However, for practical

implementation, SSP is expected to provide an early precaution of highly disaster

hazards.

(3) RPP scheme provides more precise dynamic predicted results for the overall

risk index than SSP scheme due to newest data are added into the basic set in the

GM(1, 1) model for predicting only one new unknown data. For compromise of

precaution and the precision requirement the predicted data points in RPP can be

added to 2, 3 or more.

The developed quantitative technique of dynamic risk assessment can be extended

to another applications with multiple influence factors are involved, such as

financial, social, engineering and so forth, wherein new AHP frameworks and

associated new GM(1,1) models can be built according to the treated problems.

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