Entropy-Based Set Pair Analysis Model on Geological Disaster Risk for Military Engineering *

Measuring the geological disaster-risked situation, is a typical non-deterministic decision-making issue in disaster prevention and emergency response science for military engineering. Based on the given geological disaster risk analysis mechanism, geological disaster risk monitoring matrix was established, and risk characters’ value was obtained by mining the hidden information in the monitoring matrix with Entropy theory; with Identity, Discrepancy, and Contrary of Set Pair Analysis and distance measurement, geological disaster-risked model was erected for military engineering, and the steps were given for measuring geological disaster risk, which determined geological disaster-risked SPA force and order relationship of military engineering. Finally, case showed that model has the feasibility and effectiveness over measuring the geological disaster-risked situation for military engineering.


Introduction
Geological disasters are occurred by natural or humaninduced geological environment or geology change, such as collapse, landslide, debris flow, ground fissures, land subsidence, ground collapse, sudden rock burst and the water tunnel etc. [1].
Geological disaster-risked issue was focused widely home and abroad [2], whose purpose was to estimate the damage range and potential impact of geological disaster from disaster-caused factors and pregnant environment, providing the basis for disaster prediction, disaster prevention and even disaster compensation [3].According to current study of the geological disaster-risked assessment [4], coupled structure and risk assessment logic was proposed about the possibility of the geological disaster body and the vulnerability of risk body, which gave the overall concept from the object, content, purpose and other aspects of geological disaster risk assessment.
Geological disaster was a typical threat faced by military engineering structure, whose destructive effects could easily produce the structural damage phenomenon [5], resulting in complex relationship between risk and security, so it urgently needed recognize the mechanism of geological disaster risk of military engineering, measuring the status of the geological disaster-risked military engineering, and providing support for the protective problem of military engineering.
Measurement of the geological disaster-risked situation for military engineering, has the general rules of the damage and its measurement to military engineering [6], and has the general geological disaster risk assessment rules.Otherwise, this measurement had its uniqueness, needing adapt to the corresponding standard, rule, model, method, system and etc.With SPA model, Gongshi Liang [7] characterized the geological disasters in the uncertainty of the system and its role, whose Identity, Discrepancy, and Contrary force could effectively guide the measurement of the geological disaster-risked status of military engineering, but which needed the improvement to adapt to the geological disaster control features, handling the relationship between the certainty and uncertainty of the geological disaster risk to military engineering.

Characters of Geological Disaster-Risked
Military Engineering

Risk Analysis Mechanisms of Geological Disasters about Military Engineering
Set Pair Analysis (SPA) proposed by K. Q. Zhao [8], carried on the dialectical analysis and mathematical treatment about the certainty and uncertainty within the common system, which reflected the system, differentiation, mathematical characteristics.Integration of SPA and Entropy method, tried to measure the stability of military engineering under the geological disaster risk, providing the basis for risk inspection, prevention and emergency response.
Under the geological disaster, the identification of risk class and its influencing factors was the primary work in the entire measuring process on the structure risk of military engineering, to determine the risk characteristics of geological disasters to military engineering.
With the integrated model of SPA and Information Entropy, risk analysis mechanism was established on geological disaster to military engineering, as shown in Figure 1, among which M.E.signed military engineering.
In Figure 1, the risk analysis mechanism on geological disaster for military engineering was in essence to translate the uncertainty of the geological disaster-risked military engineering into the concrete mathematical operations about Information Mining and SPA of risk monitoring information, in order to determine the overall situation and risk SPA force of military engineering.

Measure Geological Disaster-Risked Characters of Military Engineering
Following the risk analysis mechanism on geological disaster for military engineering, j C said the role of geological disaster-risked character or index to military engineering, and its set was C,  .
i said the monitoring site of military engineering, and E denoted the set of i , , , , , , x as the measurement of the military engineering monitoring site , i j x on the section of index j C , and . On the basis of the monitoring status i and ideal status of military engineering, the geological disasterrisked monitoring matrix X was erected for military engineering, such as "(1)".
where in "(1)", X was as well as called the initial monitoring matrix about the geological disaster-risked military engineering, which was the quantitative basis for all the follow-up risk analysis works.

Entropy-Based Character Weight and Distance Measurement of the Geological
Disaster-Risked Military Engineering

Standardization of Geological Disaster-Risked Characters of Military Engineering
From the perspective trends of index j C in the risk monitoring system for military engineering, there was max and min mode.Max trend showed that the greater value of j C , the more stability of military engineering; Otherwise, min trend showed that the greater value of j C , the worse stability.So, the max trend expressed the efficiency in the measurement of the geological disasterrisked military engineering status, and the min trend denoted the cost-based content. , denoted as its set, expressing the status of military engineering monitoring i .
was set as the ideal status of military engineering, whose state measurement was denoted as With the minimum method, the geological disasterrisked monitoring matrix X was standardized.If index j C showed the max trend in the risk monitoring system for military engineering, then: If index j C fo showed the min trend to in the risk moniring system r military engineering, then: Meanwhile, was defined as the of E  ine overall risk status military eng ering under the geological disasters, whose parameters were expressed as In "( 4)", the minimum value was selecte ra d as the pameter of the worst state of military engineering, which scaled the overall risk of geological hazards to military engineering of the index measurements Thus, the geological disaster risk monitoring matrix X was transformed into standardized matrix X for military engineering, such as "( 5)".

Entropy-Based Index Weight of Geological
Wei ituation

Disaster-Risked Military Engineering
ght was an important information of risk s measurement for military engineering under the effect of geological disasters, easily affected by subjective factors, where complexity and uncertainty was existed.Entropy [9] was applied into gaining the weight from the angle of the inner characteristics system and intrinsic relationship under geological disaster risk of military engineering.Entropy weight of the geological disaster risk index could reflect the disorder degree of the index system, and reduce the subjective windage effectively.
Using the standardized geological disaster risk monitoring matrix X for military engineering, , i j f was set as the proporti of the geological disaster-risked military engineering status i S on the section on j C , then: According to Information Entropy method [10,11], the Sh    ( annon entropy value was set as j e about the geological disaster-risked index j C for mi tary engineering. In " (7) f  was replaced.Thus, the weight value was determined for the geological disaster-risked index j C for military engineering, namely: where, j v denoted the weight value of the geological disaster-d index riske j C .Additionally, of the Accordingly, as the proxim to status ity from the risk status i S the worst S  , wh x ich could be e pressed as: where " and "(10)" separately expres , " (9) sed the distance measurement from the risk status to the ide and worst status i S al status S  S  , in eanin which the m g of j v consisted with "(8)".
Let dis  and dis  separately as the maximum distance measurement from the risk status i S to the ideal atus S  and overall s tus S  , as shown in "( 11

 
, , 1,2, , , That is, the risk status SPA was made up of the geological risk and the ideal status ab engineering.sa i S S  out military According to the extraction and analysis about the geological di ster-risked characteristics of military engineering, SPA i H had n features or indexes.Of these, th to the basic principle of SPA [8], ere were i al units in the identity, there were i ag units in the contrary, and there were i at units in the discrepancy of S S  and Set i S .i al , i ag , and i at must satisfy: Through the function and distance measurement of the ngineering SPA a , b , c could be

 
, i h S S  ma i i i de, as shown in "(18)".

SPA Analysis Steps about the Geological Disaster Risk of Military Engineering
There were mainly eight steps in the SPA analysis ab the geological disaster risk of military engineering.ep 1: Demonstrate the geological disaster characteristics of military engineering, and establish the geological disaster-risked monitoring matrix X.
Step 3: According to "(4)", determine the overall status (the worst status) S  of the geological disasterrisked military engineering, then establish the standardized geological disaster-risked matrix X.

Monitoring Parameters Geological Risk of Milita
Assuming under the earthquake-induced landslide ring to the emergency, rock landslides other ris characteristics [12][13][14][15], the risk features of geological military engineering was demonstrated by Single Axis Saturated Resisting Intensity, Risk Probability, maneuverability, Maximum terra stress, and others, as shown in Table 2.Meanwhile, max and min denoted the trend of the risk characteristics of the geological landslide-threatened military engineering.
Designed the important monitoring slope part of military engineering, whose status parameters were S 1 S , 2 S ,

Stan ardization and Entropy W ights
After studying on the trend of the geological disas ced landslide standardized matrix X was established for the geological disaster-risked case of military engineering with the formula "(2)" and "(3)".With "(4)", the overall geological disaster-risked landslide status S  was determined for military engineering, as shown in Table 3.
According to "(6)", "(7)", and "(8)", the dex entropy and weight value was calculated for the geological disasterris in e of geological disaste engineering was determined, as shown in Table 5.
A ximum distance of geological disa ulated as gical n accordanc with 18)" a PA coefficients and force was determined for the geological disasn in Table According to r-risk case on military k case for military engineering, as shown in Table 4.

Distance of the Geological Disaster-Risked Military Engineering Case
In accordance with the "(9)", "(10)", "(16)", the distanc ccording to the "(11)", the ma ster-risk case was calc 0.198 dis   , 0.0664 dis   ., which reflected the degree of the ge gi disasterrisked military engineering was in the weak contrary force, and viewed the general risk threat.or the geolog cal disaster-ris ed sections o military engineering, which could relief conflicts between emergences resource and engineering requirement, providing relevant helps to organize or command the repair problem.

Conclusio
1) A brief analysis to the value of the geological risk measurement of military engineering, put forward the measuring features of geological disaster-risked status of military engineering; The exploration to the characteristic of index parameters and variation trend, proposed the andardized method for risk index parameters, and established the standardized matrix of geological disaster-2) SPA model of the geological disaster-risked military engineering, put forward the work steps for the geological disaster-risked SPA status of military engineering, and quantitatively analyzed the certainty and uncertainty between the monitoring section and ideal status of the geological disaster-risked military engineering.eological di ring.However, how to evaluate the co

Figure 1 .
Figure 1.Risk analysis mechanism on geological disaster for military engineering.

Distance Measurement of the Geological Disaster-Risked Military Engineering
3.3.i could be weighted by Minkowski distance, namely:

. Coefficient Calculation about Military Engineering's Geological Disa SPA
i al n was identity, i at n was discrepancy, and

Table 1 . Geological risked SPA force degree and order relationship on military engineering.
i c .Step 8: Calculate the force i Shi H of the geological disaster-risked military engineering SPA, select the corr sponding degree fro Table1, analyze the overall disaster-

Table 1 ,
E and 3 E m