LIU Yi(刘义)，SUN Xu(孙旭)，CHEN Jun(陈军)，AN Xin-yuan(安新源)

(1.Unit No.63880，Luoyang 471003，Henan，China;2.College of Electronic Science and Engineering，National University of Defense Technology，Changsha 410073，Hunan，China)

Introduction

Effectiveness evaluation of anti-radiation weapons is an indispensable step in the development and deployment of weapons［1－2］.With the development of anti-radiation weapons，the effectiveness evaluation of anti-radiation weapons has been turned from the simple accuracy index to the integrated countermeasure capability.The research priority is how to access the combat effectiveness of anti-radiation weapons in the complex countermeasure environment. At present， the effectiveness concept and framework which were developed by weapon system effectiveness industry advisory committee(WSEIAC)for US air force are used for the most evaluations of weapon systems.WSEIAC defines any system:system effectiveness is a measure that satisfies(or accomplishes)a set of tasks.This definition includes 5 elements:object，task，condition，time and ability.Since the target range tests are always done for real weapon systems，they can reflect the actual combat environment realistically，and provide data for quantitative analysis of relative issues.When the weapon effectiveness is evaluated through the target range test，first four elements corresponding to WSEIAC’s five elements are known.The last element should be described using test data.That is to say，the target range test and evaluation of weapon effectiveness is to evaluate the ability of specific object to complete a specific task at specific time and in specific condition［3］.

For the present situation of target range test and the characteristics of anti-radiation weapons，a combat effectiveness assessment model based on non-linear index aggregation was proposed for anti-radiation weapons.A corresponding index system model，index aggregation methods and an index weight determination were given in the paper.Finally，the simulation results verify that the proposed method solve the combat effectiveness assessment of anti-radiation weapons effectively.

1 Target Range Test of Anti-radiation Weapons

For anti-radiation weapon，its effectiveness is sensitive to the battlefield environment and may be affected greatly by the complexity of electromagnetic environ-ment.The target range test of anti-radiation weapons，which is to test the ability of anti-radiation weapons to complete the specific tasks in electromagnetic countermeasure environment at different levels，needs a mass of data as its evaluation basis.Since the anti-radiation weapon mostly attacks the radar positions，it is unscientific and irrationalto evaluate itseffectiveness through live cartridge test.Moreover，the live cartridge test may cause needless waste and can’t provide enough data to support the evaluation.In order to solve the problem of lacking data，the target range test of anti-radiation weapon includes ground test，flight test and target practice test.After a great deal of countermeasure test data is collected during the ground test and the flight test，the collected data are validated and the entire performance of weapon system is assessed during the target practice test.

1.1 Ground Test

Ground test has obvious advantages of high precision，low cost and convenient-to-operation and high repeatability.Furthermore，the handling process of seeker can be observed during the test，the data is easily captured，and the measured error is small.The working status and anti-jamming ability of anti-radiation weapon in different electromagnetic environments can be grasped entirely by flexibly setting the radar defense.In the ground test，the high tower test mode is always used to simulate the air-to-ground status of antiradiation weapon.However，in the ground test，the radiation source and the seeker are in a state of relative rest，which is much different to a real combat environment.Thus，the results of ground test are of low representativeness and credibility，which are usually used to analyze the anti-jamming performance and guidance ability of anti-radiation weapons.Ground test is the basis of flight test and target practice test.

1.2 Flight Test

In different electromagnetic interference backgrounds，the effectiveness of anti-radiation weapon is much different. However， since the anti-radiation weapon mostly attacks the ground fixed targets at high altitude or low altitude，the terminal phase of 2 000 m in which it attacks is an approximate conic line，and the errors due to simulating attack fitting are small.Moreover，the terminalguidance ofanti-radiation weapon determines its attack precision，that is to say，in the countermeasure test，what is concerned about anti-radiation weapon is the reconnaissance and direction finding of seeker in the diving attack phase(2 000 m－200 m).The effect close to actual combat can be reached by simulating the terminal phase of anti-radiation weapon in the flight test.Compared to the ground test，the flight test is more close to the real situation and the test result is credible.However，the flight cost is so high that the anti-radiation weapon can not test in every countermeasure environments in the condition of limited manpower and resources.On the basis of ground test，the effectiveness of anti-radiation weapon is usually tested and evaluated in typical scenes.

1.3 Target Practice Test

In the target practice test，the baiting systems and the protected radars are deployed，and the anti-radiation weapons are breakthrough and target practice according to actual operation requirements.This test is the highest form of target range tests，which is usually used as the last test.It can validate the integrated effectiveness of anti-radiation weapon systems effectively.However，it can’t be executed for many times due to its high cost，the various countermeasure situations are considered，and the sufficient data can not be also obtained.Furthermore，the final indexes，such as breakthrough probability and hit accuracy，can be got from the target practice test，but the results of process node in the signal processing of anti-radiation weapon can not be obtained from it.

1.4 Environment Setting

The operational environment has influence on the effectiveness of anti-radiation weapon.It is necessary to build the range test environments with different complexity and test its effectiveness in the different electromagnetic environments.In the paper，the complexity of electromagnetic environment into four classes:

1)Radar has a higher radiation power and a broad radiation beam，and only uses an advanced turnoff technology.

2)High gain and narrow beam radar antenna，alternative boot-strap and frequency hopping are used.

3)Based on the above electromagnetic counter-measure technologies，the active decoying interference technology is added，the radars are netted，and the multi-field radar alternative on-off and wide range frequency agility technologies are used.

4)All the technologies above are used，the infrared decoy is used to jam the missile which uses the infrared identification technology in terminal guidance，the false target decoy is used to jam the missile which uses the image identification technology in terminal guidance，the on-the move on-off technology of vehicular radar and the multi-base antenna system and mirror effect for jamming are used.

2 Test and Evaluation Approach of Anti-radiation Weapon Effectiveness

Ground test，flight test and target practice test are the common forms of test and evaluation approach for anti-radiation weapon，and each test has its own advantages and disadvantages.In order to evaluate the effectiveness of anti-radiation weapon actually，all of the three are used.How to integrate the results of the three tests and give a rational and scientific evaluation is a problem that should be solved in the development of target range test technology.A combat effectiveness assessment model based on non-linear index aggregation is proposed for anti-radiation weapon.Moreover，the target range test features of anti-radiation weapon are fully considered in this paper.The corresponding index system model，index aggregation methods，index weight determination and index appraisal methods are described hereafter.

2.1 Multi-level Index Evaluation System

Multi-level index system which reflects the hiberarchy characteristic of thinking mode can divide a complex problem into step and layered ordered structure，and simplify the problem.The manner that the expert appraisal method forms a discrimination matrix to determine weight in the same time not only integrates the experiences of experts，but also indicates the combining feature of qualitative method and quantitative method.The selected index should inflect the main function of weapon，markedly affect its effectiveness，and show the differences of weapon effectiveness in different environments and different tactics.These indexes which have obvious physical meaning and military significance can be measured by means of modeling quantitative solving and simulation test.Since the actual situation is complex and changing，the index system is usually composed of multi-level indexes.The superlevel indexes can be captured by aggregating the sublevel indexes.As shown in Fig.1，the index system of target range evaluation of anti-radiation weapon effectiveness is given by integrating the features of three test methods(ground test，flight test and target practice test).

2.2 Index Aggregation Methods

Currently，the analytic hierarchy process(AHP)is usually adopted for index aggregation in the effectiveness evaluation of weapon.AHP can divide a complex problem into step and layered ordered structure，simplifies the problem，and reflects the hiberarchy characteristic of thinking mode.However，this method simplifies the aggregation between the levels of the index system so much that there is only weighted sum mode.In other words，only‘or’relation between sublevel indexes is considered and the index weight reflects the contribution of sub-level indexes to the superlevel indexes.In effectiveness evaluation，some sublevel indexes are aggregated to the super-lelvel indexes in term of‘and’.That is to say，for super-level indexes，each sublevel index is a pivotal factor.The effectiveness is zero if one of the sub-level indexes is zero.For‘ground test effectiveness evaluation(v1)’in Fig.1，the effectiveness of missile system is described by the destruction(or kill)probability for specified target.But in ground test，the destruction probability can not be captured，and the effectiveness evaluation is formed by aggregating the effectiveness of every node in seeker working flow.Sub-level indexes，including‘ability of target signal interceptor(v11)’，‘ability of target signal discrimination(v12)’，‘ability of missiletarget information measurement(v13)’，‘ability of command and control signal generation(v14)’，are the critical factors for super-level indexes.If anyone of the sub-level indexes is zero，the effectiveness of super-level indexes is zero.Here，only weighted sum can not reflect the manner of index aggregation.This paper proposed two methods of index aggregation:‘and’relation，weighted sum and ‘or’relation，weighted product.In Fig.1，‘⊕’and’⊗’represent the aggregation of sub-level indexes to the super-level indexes.‘⊕’represents the aggregation of sub-level indexes to the super-level indexes in the manner of‘or’，while‘⊗’represents the aggregation of sub-level indexes to the super-level indexes in the manner of‘and’.

Fig.1 The index system model of anti-radiation weapon

2.2.1 ‘or’Relation

The relationship between sub-level indexes is‘or’.The sub-level indexes are aggregated to the upper level by weighted sum.The weight here presents the importance of child indexes for their father indexes.Higher the importance is，greater the weight of the child indexes is.

where riis a super-level index，rijis the sub-level index slaving to ri，ωijis the weight corresponding to rij.

2.2.2 ‘and’Relation

The relationship between sub-levelindex is‘and’.The sub-level indexes are aggregated to upper level by weighted product.Here，every sub-level index is essential for the super-level indexes.If one of the sub-level indexes is zero，the polymerized super-level index is zero.The weight here presents the effect of child index on the father index when the child index changes.Higher the importance is，greater the weight of the child indicator is.

where riis a super-level index，rijis the sub-level index slaving to ri，ωijis the weight corresponding to rij.

2.3 Method for Weight Determination

There are two methods for weight determination:subjective weight determination and objective weight determination.In practice，in order to overcome human factors，it is usual to combine the two methods.With reference to Ref.［6，8］，this paper adopts the method of organizing p experts to subjectively determine the weight of each class according to the tactics，technology and main usage mode of equipment，and then integrates these weights to get the weight of each index.Suppose that p experts determine the weight of n indexes as xij，

Eq.(3)is used to calculate the correlation coefficient ζjk，and then get the correlation matrix A(ζjk).Calculate weight determination as Eq.(4):

Thus，the weight of the ith index is

2.4 Grading Method for Evaluation Indicator

The basic rule of grading in the target range test evaluation of weapon effectiveness is that the capability magnitude to accomplish specific task in specific condition.In order to do quantitative description，the war requirement is taken as the grading rule.

According to the basic rule，the indexes can be divided into quantitative indexes and qualitative indexes.The quantitative indexes can be calculated by data，while the qualitative indexes can not be calculated by data，which can only be described by the qualitative messages such as‘high，middle，low’，‘excellent，fine，middle，pass…’，etc.the subjective grading and objective grading methods can be used for quantitative indicator and qualitative indicator.

2.4.1 Objective Grading Method

The objective grading method is used for quantitative indicator.If the data of a certain quantitative index Vmnachieved in mission is dmn，its grade is:

where dmnois the ability of index required.Obviously，dmn≤dmno.Thus 0≤rmn≤1.

As shown in Fig.1，v111is the ability of target signal interceptor with one-level electromagnetic environment in ground test.Interceptor probability can be captured by a mass of ground Monte Carlo tests.Therefore，it can be graded using objective grading method.

Example 1suppose that the index requirement of weapon interceptor probability is 95%，and the interceptor probability get by ground Monte Carlo tests is 87%.Thus the objective grade is:

2.4.2 Subjective Grading Method

The objective grading method is used for quantitative indicator.Since the qualitative indexes can not get a specific value from data，they are always achieved by experts’qualitative evaluation.In order to aggregate the indexes，the qualitative evaluation should be quantized.Both gray theory［6］and fuzzy theory［7］can quantize the qualitative messages.With reference to Ref.［6］，this paper uses the qualitative message quantization method of gray theory.

Definition 1Suppose that there are n qualitative rank gray variants:x(1)，x(2)，…，x(n)corresponding to‘excellent，fine，middle，…’qualitative messages，and f is mapping，f:x(k)→μk，thus

where f［x(n)］is the linear whitening weight function of qualitative rank gray variant.

Definition 2Suppose that the interval gray variant is x∈［a，b］and f is mapping:

where 0≤α≤1 is called decision-making weight coefficient，which can be determined by the preference of the decision-makers;f(x)is the linear whitening weight function of x in ［a，b］.For α =0.5，

A qualitative indicator vijis subjectively graded.First of all，the qualitative evaluation set of n ranks is determined according to the experts and the indexes，and organize p experts to grade the weapon according to the set to get the original qualitative evaluation set:

The original qualitative evaluation set is quantized according to Definition 1:

The grade of vijis got by averaging the quantized evaluation opinions:

obviously，0≤rij≤1.

As shown in Fig.1，v31is the maneuverability of missile in target practice test.Since the number of target practice test is limited，the objectiveness with large amount of data can not be achieved.Thus，this index is graded by the subjective grading method.

Example 2v31is graded by the subjective grading method.Suppose that there are 5 qualitative gray variants x(1)，x(2)，…，x(5)，corresponding to‘excellent，fine，middle，relative poor，poor’5 qualitative evaluation sets.

As shown in Tab.1，5 experts are organized to grade v31，and the original evaluation opinions are quantized by Definition 1.

Tab.1 Indexes-subjective appraisal

The subjective grade of v31can be calculated by Eq.(13):

3 Example of Evaluation Simulation of Anti-radiation Weapon in Target Range Test

3.1 Calculation of Effectiveness Evaluation Weight

According to the index system shown in Fig.1，4 experts are organized to present the weight of every index.

Tab.2 Weight assignment of indexes

Tab.2 only shows the weights of bottom indexes.Since the weights of other bottom indexes are the same in the same electromagnetic environment with the same test mode.According to Eq.(10)，(11)and(12)，the weights are calculated to get the weight of every level indicator in the evaluation system.

Tab.3 Calculated index weights

3.2 The Combat Appraises Class of Anti-radiation Weapon Effectiveness

The combat appraises class are defined according to the effectiveness of anti-radiation weapon.

Tab.4 The combat appraises class

3.3 Evaluation of Anti-radiation Weapon Effectiveness

The bottom indexes are graded by the method introduced in Section 2.4.

Tab.5 The bottom index aggregation-results

The bottom indexes are aggregated to get the middle indexes level by level，and finally get the top-level indexes.

Tab.6 Index aggregation

The effectiveness evaluation of anti-radiation weapon in the target range test obtained by index aggregation is v=0.648 3.Based on the definition of the combat appraises class，this weapon is evaluated‘fine’.

4 Conclusions

In view of the present situation of target range test and the characteristics of anti-radiation weapons，a combat effectiveness assessment model based on nonlinear index aggregation was proposed for anti-radiation weapons.This model aggregates the indexes by‘or’and‘and’，and can reflect the logic relation between indexes in super-level and sub-level.Furthermore，the method for bottom index determination and the method for index weight determination were introduced in this paper.Finally，the simulation results verify that the proposed method can effectively solve the combat effectiveness assessment issues of anti-radiation weapons.

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