A probabilistic fuzzy method for emitter identification based on genetic algorithm

Transcription

1 A probabitic fuzzy method for emitter identification based on genetic agorithm Xia Chen, Weidong Hu, Hongwen Yang, Min Tang ATR Key Lab, Coege of Eectronic Science and Engineering Nationa University of Defense Technoogy Changsha 47, P.R. China Abstract Th paper presents a probabitic fuzzy method for emitter identification (EID) based on the data-driven mode. The input attributes of the EID probem incude the radio frequency (RF), puse repetition interva (PRI), puse width (PW), etc. Given a fuzzy partition of the input attributes, a method for deriving a set of probabitic fuzzy rues from training data presented. With the aid of genetic agorithm (GA), the fuzzy partition can be adusted to achieve high cassification accuracy and good interpretabiity simutaneousy. Data-driven candidate of fuzzy partitions of the input space adopted, which guarantees the interpretabiity of the resuting rues and enabes GA to find good fuzzy partition quicky. The experimenta resuts show high performance of the proposed method. Keywords- emitter identification; fuzzy rue-based cassification system; fuzzy partition; genetic agorithm I. INTRODUCTION The EID one of the primary functions of radar warning receivers. In miitary operation, EID, which usuay invoved in an eectronic support measure system, can provide a usefu means to identify the hostie radar. For the EID probem, if the attribute parameters of the measured emitters are known in advance, the remaining task to design a cassifier to dtinguh one type of emitter from another. A number of conventiona pattern recognition methods incuding Bayesian cassification [], k-nearest neighbor cassification [2], and neura network [] are appied successfuy in recent years. Besides these methods, fuzzy rue-based technique [4] an idea too to dea with the EID probem. As one type of modefree methods in soft computing, fuzzy rue-based techniques are extensivey used in modeing noninear and compex systems. Fuzzy method an effective way to dea with the uncertainties of the training data, and the freedom of fuzzy partitions for the EID input attributes considered to be more fexibe to hande the uncertainty in rea situations. In practice, the uncertainties EID faced can be divided into three categories: one about the continuous attribute uncertainty measured in emitter signas, such as RF, PRI, PW, etc. Because these continuous attributes measured by the radar warning receiver aways have warps compared to their true vaues; the second about the uncertainty of incompete knowedge in the training sampes. The working modes and the parameters themseves are various, so it impractica to obtain a the working parameters of the emitters; the third about the uncertainty of some descriptive attributes. For exampe, different beief masses may be assigned to the attribute of intra-puse moduations. In th paper, we mainy focus on designing a fuzzy rue-based system to process the first two cases of the uncertainties. A ot of efforts have been done in designing fuzzy ruebased systems, but many of them generate rues with the determintic consequences. The uncertainties residing in the reasoning part are generay ignored. In fact, randomness of the input-output training data pairs exts in the training sampes of the EID probem. The uncertainties infuence the identification accuracy significanty, and the conventiona determintic consequences of the rue are no onger competent for such cases. It desirabe to use probabitic fuzzy rues instead of conventiona ones by assigning a probabiity to each possibe consequence of the rue. In such a manner, the uncertainty of the EID probem can be appropriatey modeed and effectivey treated. To dea with the uncertainties of the EID probem, two factors shoud be considered in constructing the fuzzy ruebased mode. One the fuzzy partition of each input attribute, and the other the membership function used on the fuzzy partitions. Fuzzy partitions go hand in hand with the dtribution of the EID training data, so it reasonabe to use GA [5-] as an effective method to find the optimization of the fuzzy partitions by seecting the eitt individuas in each evoutiona generation. In order to keep things as simpe as possibe, ony trapezoida and trianguar membership functions are used on the fuzzy partitions. A method for generating a set of probabitic fuzzy rues from abeed data of emitter signas presented in th paper, which cooperates with the GA-based adustment of fuzzy partition to derive accurate and interpretabe fuzzy cassifiers. Specificay, a set of rues corresponding with subgroups of data are induced for each given fuzzy partition. The candidate fuzzy partitions are determined by the data, which assume the form of strong fuzzy partitions. Accurate and interpretabe fuzzy cassifiers are generated by searching comprehensibe fuzzy partitions in the candidate space using GA. An experimenta study invoving the five-eid probem without and with measurement noe carried out, which shows the good performance of the proposed method. 65

2 The remainder of th paper organized as foows. Section II gives the EID probem formuation, and the steps of fuzzy rue generation as we as fuzzy reasoning are described in detai. The fuzzy partition of emitter attributes and the GAbased optimization of fuzzy partition are proposed in section III. In section IV, experiments are studied and the resuts are anayzed. Concusions are drawn in section V. II. PROBLEM FORMULATION The obective of EID to infer emitter type by matching the measured parameters with the known emitters in the database, which stores the parameters information of emitter types and can be used to generate fuzzy rues for identification processing. Here, the emitter attributes RF, PRI, and PW are chosen to form a state vector [x,, x ] in a three-dimensiona space. Emitter parameters and performance are affected by the RF band in which they operate. Likewe, the range of frequency band chosen for a specific emitter determined by the radar s msion and specifications. By comparing the frequency of the received puses, the puse trains can be sorted out and identified for different radars. The parameter PRI the time difference between the eading edge of consecutive transmsion waves, and it the reciproca of puse repetition frequency. The PRI varies for different radars. Another parameter PW can be used to provide coarse information on the type of radars. For exampe, weapon radars usuay have short puses []. In practice, dturbances occur in these continuous attributes due to the compexity of the eectromagnetic environment, and the known emitter data base can not cover a the working parameters of the emitters. It appropriate to use fuzzy sets to represent each emitter attribute of the known data base in the form of fuzzy membership function on fuzzy partitions. The freedom ying in the interva of fuzzy partitions and the degree of membership functions provides a fexibe description of the data dtribution uncertainties. Assume that there are N abeed patterns of signa attributes { x i x i ( x i, x i, x i ; C ), i,..., N} from k emitter types as 2 i training data, where x i the vaue of the th attribute in the ith training pattern. C i {c,,c k } the corresponding type abe. Given a measurement pattern x=(x,,x n ), udging the emitter type of x from the training patterns a noninear mapping probem, which can be approximated by a probabitic fuzzy ogic system. A. Fuzzy Rue Generation For the training data { x i x i ( x i, x i 2, x i ; Ci ), i,..., N} from emitter sampes, the fuzzy rue construction as foows: ) Estabhment of fuzzy partitions of emitter attributes. Let [ x, x ], [ x2, x2], and [ x, x ] be the domain intervas of RF, PRI, and PW, respectivey. Where domain interva of an attribute means that most probaby th attribute wi take vaues in th interva. For identification probems, the domain interva of each attribute can be identified as the interva formed by the minimum and maximum vaues of training patterns under that attribute. Divide each domain interva into a number of fuzzy regions, denoted by some anguage abes ike SK (Sma K),, S (Sma ), CE (Center), B (Big ),, BQ (Big Q), which are represented by corresponding fuzzy sets. In th partitioning process, different attributes may have different numbers of fuzzy regions. It required that these fuzzy sets must be compete in respective universe of dcourse. Suppose that the domain interva of input variabe x i partitioned into M i fuzzy sets represented by A (x i ),,A M (x i ). The partition considered to be compete in the universe U if xi U, i M, st.. Ai( xi). Fig. shows an exampe where the domain interva of x divided into five fuzzy regions, the domain interva of divided into seven fuzzy regions, and the domain interva of x divided into five fuzzy regions. The fuzzy partitions of emitter attributes have a cose reation with the cassification accuracy and interpretabiity of the subsequent generated rues. The optimization of fuzzy partition detaied in section III. m(x) m(x2) m(x) S2 S CE B B2 x - + x x x Figure. Fuzzy partitions and memberships (a) S S2 S CE B B2 B - 2 (b) S2 S CE B B2 x - x + x x (c) 2) Grouping of emitter training data. For given fuzzy partitions of emitter attributes, cacuate the i i i membership degrees of x, x 2, and x, i,..., N in i i different fuzzy regions respectivey. Assign x, x 2, i and x to the region with the maximum degree. B in Fig. (a) associated with x, S in Fig. (b) associated with x 2, and S in Fig. (c) associated with x. These trianguar regions compre the antecedents of the fuzzy cassification rues to be derived. For the abeed patterns, it possibe that different patterns associate with the same antecedent of fuzzy sets. Thus the patterns can be cassified into groups such that each shares the same antecedent fuzzy sets. For exampe, ( x, x2, x ) and ( x, x2, x ) in Fig. are in the same group. Suppose that L groups are + 66

3 formed and the corresponding antecedent fuzzy sets can be expressed by A, A 2, and A (=,, L). ) Construct EID cassification rues based on the formed groups. where t If x A and x A and x A, (,..., ),,..., 2 2 r rk L r cacuated by t t t 2 2 t t t A( x) A2( x2) A( x) Ct c r,,..., L,,..., k N A ( x ) A ( x ) A ( x ) To th end, a probabitic fuzzy rue base for EID obtained from the data set, based on which the probabitic fuzzy reasoning can be impemented. It observed that the way of partitioning emitter attributes has a direct effect on the performance of the resuting fuzzy cassifier. In section III, a GA-based method for fuzzy partition optimization presented. B. Fuzzy Reasoning Method Suppose the fuzzy rue base composed of L rues. For a p p p p measurement pattern of emitter x ( x, x2, x ), the fuzzy reasoning method introduced in [2] adopted. The procedure described in the foowing steps ) Matching degree cacuation. The matching degree the strength of activation of the if-part for a rues in the rue base with the pattern x p. A T-norm empoyed p p p p to compute it. R( x ) T( A( x ), A2( x2 ), A( x )). The min T-norm used in th study. 2) Association degree cacuation. The association degree b of pattern x p with c under the th rue p obtained by combining R ( x ) and r with an aggregation operator h, b ( ( p ), h R x r), where h can be the min, product operators. The product operator used here. ) Pattern cassification soundness degree for a casses. Computing the soundness degree Y of pattern x p with c, Y f( b,,..., L, b ), f being an aggregation operator verifying min f max. The Badd operator adopted in th study, i.e., L t ( ) b f( b,..., bl ), t 2. L t ( b ) 4) Cassification. Assign the measurement pattern of signa attributes x p ( x p, x p 2, x p ) to the emitter type c m such that m Argmax{ Y },,..., k. III. FUZZY PARTITION OPTIMIZATION USING GENETIC ALGORITHM The we known and widey used GA a goba search technique which foows the principe of bioogica evoution and genetics. The abiity of GA to expore a arge search space for suitabe soutions ony requiring a performance measure makes it an efficient method for soving compicated optimization probems. As mentioned above, the performance of the presented fuzzy cassifier depends on the fuzzy partitions of emitter attributes. In order to improve the identification capabiity, the GA used to search for good fuzzy partitions. A data-driven candidate space of fuzzy partitions adopted, which keeps the resuting fuzzy rues interpretabe. A. Coding of Fuzzy Partition The candidate space of fuzzy partitions determined by the set of training patterns using a technique utiized in []. The coding scheme demonstrated by a simpe exampe as foows. Suppose the dtribution of patterns of RF as in Fig. 2. (The emitter attribute vaues are normaized to [,]). Membership Emitter Emitter 2 Emitter A B C D E F G H Figure 2. Pattern dtribution on RF Figure. One candidate fuzzy partition for RF Here 6 abeed patterns coming from emitters are assumed. First the domain interva of each attribute subdivided into intervas such that each incudes training patterns from the same emitter type as many as possibe (see A, B, F, G, H in Fig. 2). When an interva can not incude mutipe training patterns from the same cass, the interva degenerated as a point (see E in Fig. 2). If there are mutipe patterns from different casses at the same position, that RF 67

4 position aso handed as a degenerated point (see C and D in Fig. 2). The domain interva of the RF attribute subdivided into eight intervas in th exampe. Each interva considered as a candidate position where a trapezoida membership function paced. In the case of a degenerated interva, a trianguar membership function paced. Seecting a group of candidate positions and constructing corresponding membership functions, a fuzzy partition of the RF attribute obtained. One choices, (A, C, D, F, H), shown in Fig.. The membership functions at the eft and right end positions are expanded to and with membership respectivey. The strong fuzzy partition adopted for each emitter attribute using the seected positions. A binary string can be used for fuzzy partition coding of each emitter attribute. The ength of the string the number of the candidate positions. If the position seected for partition, encode it as ; otherwe, encode it as. The code corresponding with Fig.. Th fuzzy partition technique guarantees the interpretabiity of resuting fuzzy sets, which aso makes the generated fuzzy rues understandabe. When the number of s in a code string ess than two, the attribute described by a singe unity membership function on [,] which can be understood as don t care. If th kind of code obtained for a certain attribute, th attribute useess for the process of emitter identification, because the singe membership function makes no differentiation to a the possibe attribute vaues. Thus the number of input variabes in rues reduced consequenty. Since the candidate partitions of emitter attributes are determined by the dtribution of training patterns, the number of candidate positions for each attribute may be different. Let the code ength of the ith attribute be i, and the candidate fuzzy partition of the attribute coded by S i. Then, the fuzzy partition of a the attributes represented by a concatenated string S=S S 2 S. Given the fuzzy partition S, a fuzzy cassifier can be derived from training patterns as addressed in section II. Therefore, the identification capabiity of the cassification system can be optimized by adusting the fuzzy partition S. B. Optimization of Fuzzy Partition In order to find a good fuzzy partition of emitter attributes such that the generated fuzzy cassifier based on the training set achieves high prediction accuracy, the identification capabiity of the fuzzy cassifier can be evauated with a fuzzy partition in the foowing way. Let the training set be E. Randomy divide E into two subgroups A and B (with probabiity 5%-5%). For a given fuzzy partition of emitter attributes S, the fuzzy cassifier can be induced from A using the method presented in section II, which used to cassify patterns in B. Let the cassification accuracy be p(s). Simiary, a fuzzy cassifier can be induced from B, which used to cassify patterns in A. Let the cassification accuracy be p2(s). The average cassification accuracy p(s)=(p(s)+p2(s))/2 used for evauating the identification capabiity of the fuzzy cassifier corresponding with S. The GA used for fuzzy partition adustment to improve the identification capabiity of the resuting fuzzy cassifier. The steps are as foows. ) Popuation initiaization. Generate an initia popuation of J individuas. or randomy assigned to the i positions of substring S i, i=,2, of each individua S. 2) Seection. Let the popuation of the mth generation denoted by m, and p(s) be the evauation of the identification capabiity for fuzzy cassifier induced from S m based on the training set E. Seect J/2 pairs of individuas from m according to the foowing seection probabiity Q(S). QS ps ( ) p ( ) min m ( ), { ps ( ) pmin ( m )} Sm where p ( ) min ( ) min p S. m Sm S m ) Crossover. For each of the seected pairs of individuas, randomy seect a integer q{2,} and interchange the substrings from the qth attribute to the ast attribute with probabiity P corss. Let SSS 2 and SSS be a pair of seected individuas, SSS and SSS may be obtained after the interchange ) Mutation. Two mutation operators are sequentiay appied to individuas generated by the crossover operation. One interchanges the neighboring bits in each substring S i with probabiity P oca ; the other reverses the vaue of each bit with a given probabiity P reverse. 5) Eitt strategy. Repace a randomy seected individua in the current popuation with the best individua in the previous popuation. 6) Termination test. Terminate the agorithm if the stopping condition satfied. Otherwe, return to step 2). The vaue of p max =max{p(s)}, S m used to terminate the agorithm in th study. It generay required that P reverse ()>P reverse () in step 4) to reduce the number of fuzzy regions for each emitter attribute. IV. EXPERIMENTAL STUDY In th section, the EID performance of the proposed fuzzy cassifier compared with the new vector-type back propagation (NVTBP) agorithm [4] and combination of vector neura networks (CVNN) agorithm [5] on the same training and testing sampes. A training and testing sampes are from the emitter sampes repository, which stores the measured emitter of five types. The parameter attributes of the emitter sampes are RF, PRI and PW, part of the training and testing sampes are ted in Tabe I and II, respectivey. In practica situation, it noted that the number of cassification rues are in proportion to the number of different emitter types. 68

5 TABLE I. PART OF THE TRAINING SAMPLES Emitter Type RF, GHz PRI, s PW, s Emitter Type TABLE II. PART OF THE TESTING SAMPLES RF, GHz PRI, s PW, s As a preprocessing of the data sets for the fuzzy cassifier system, each parameter domain of emitter attributes normaized to the unit interva [,]. The parameters of GA are specified to optimize the fuzzy partition in fuzzy cassifier design. Suppose the patterns in the data set are from k types. Each fuzzy partition of the pattern space encoded as S=S S 2 S, where S i the coding of the ith attribute with ength i. In the initiaization step, randomy assigned with the probabiity k/ i, and randomy assigned with the probabiity -k/ i. The popuation size J=, the crossover probabiity P cross =, the mutation probabiity P oca =., P reverse ()=., P reverse ()=., and the termination condition p max =. A. Performance Evauation Without Measurement Noe In th subsection, ten trias for the EID probem are considered. In each tria, 2 sampes containing five emitter types are randomy seected from the emitter sampe repository. 5 sampes are used for training and a remaining sampes are used for testing (each emitter has ten training sampes and thirty testing sampes). The average cassification rate cacuated over the ten trias. One fuzzy partition that eads to a five-rue cassifier with the cassification rate % in the ast generation of one tria shown in Fig. 4; the induced rues are dpayed in Fig x x Figure 4. The fuzzy partition of the input attributes If x.5 If x.5.5 If x.5 If x If x Figure 5. The induced fuzzy rues The number of fuzzy partitions of each attribute and the number of generated rues are two main factors affecting the interpretabiity of fuzzy cassification systems. For the five- EID experiments, at most three fuzzy sets are used in the strong fuzzy partitions of attributes, which foows the 7±2 principe of imits on human capacity for processing information. Moreover, a membership function that aways equas to signifies that the corresponding attribute not used in the 69

6 generated rues, such as x in Fig. 4. Thus, the generated rues are compactabe and interpretabe. B. Performance Evauation With Measurement Noe In order to evauate the robustness of the proposed fuzzy cassifier, the measurement dtortion simuated by adding noe. To perform the testing at different eves of adding noe, the error deviation eve (EDL) defined by pi EDLi (%) %, i,2, x pi where x pi the data without noe and pi random noe. If the testing sampe without adding noe x p =(x p, x p2, x p ), and p =( p, p2, p ) the random noe corresponding to x p, the noy testing sampe wi be (x p ± p, x p2 ± p2, x p ± p ). In th experiment, the noy testing sampes with different EDLs (from 2% to 2%) are presented to the trained fuzzy cassifier for performance testing. The resuts are ted in Tabe III. The experimenta resuts indicate that, compared with the NVTBP agorithm and the CVNN agorithm, the proposed method makes the resuting cassification rues interpretabe and comprehensibe by generating fuzzy partitions according to the dtribution of training data. Moreover, there a ot of freedom in choosing the vertices of membership functions by the GA-based fuzzy partition adustment, so the proposed fuzzy cassifier has universa superiority in both high and ow noy environments. TABLE III. Error deviation eve% 5-EID PROBLEM WITH NOISE (-RUN AVERAGE) NVTBP CVNN agorithm agorithm Average identification rate% Fuzzy cassifier V. CONCLUSIONS In th paper, a probabitic fuzzy rue-based cassification system for EID has been designed, together with the GA-based fuzzy partition adustment to improve the system performance. The candidate space of fuzzy partitions determined by the data dtribution, which makes the evoved fuzzy partition interpretabe and therefore the resuting rues comprehensibe. The experimenta resuts show good earning capabiity of the proposed method. As future work, it woud be of interest to investigate the use of instance seection technique [6] to dea with muti-eid probems having both high dimensiona attributes and arge number of sampes. Moreover, the termination condition of GA another topic deserving continuing efforts. REFERENCES [] Q Huo, and C. H. Lee, A Bayesian predictive cassification approach to robust speech recognition, IEEE Transactions on Speech Audio Processing, vo.8, no.2, 2, pp [2] B. Zhang, and S.N. Srihari, Fast k-nearest neighbor cassification using custer-based trees, IEEE Transactions on Pattern Anayzing, Maching, and Inteigence, vo.26, no.4, 2, pp [] G.B. Wison, Radar cassification using a neura network, Procedings of Appied Artificia Neura Networks, SPIE, 99, pp [4] S.A. Hassan, A.I. Bhatti, and A. Latif, Emitter recognition using fuzzy inference system, Proc. IEEE Internatina Symposium Emerging Technoogies, Isamabad, Paktan, 25, pp [5] Y.C. Hu, Finding usefu fuzzy concepts for pattern cassification using genetic agorithm, Information Sciences, vo.75, no., 25, pp. 9. [6] M.Q. Li, and Z.C. Wang, A hybrid coevoutionary agorithm for designing fuzzy cassifiers, Information Sciences, vo.79, no., 29, pp [7] H. Ishibuchi, T. Yamamoto, and T. Nakashima, Hybridization of fuzzy GBML approaches for pattern cassification probems, IEEE Transactions on Systems, Man, and Cybernetics, Part B, vo.5, no.2, 25, pp [8] H. Ishibuchi, and Y. Noima, Anays of interpretabiity-accuracy tradeoff of fuzzy systems by mutiobective fuzzy genetics-based machine earning, Internationa Journa of Approximate Reasoning, vo.44, no., 27, pp. 4. [9] M.J. de Jesus, F. Hoffmann, L.J. Navascués, and L. Sánchez, Induction of fuzzy-rue-based cassifiers with evoutionary boosting agorithms, IEEE Transactions on Fuzzy Systems, vo.2, no., 24, pp [] F. Hoffmann, B. Baesens, C. Mues, and J. Vanthienen, Inferring descriptive and approximate fuzzy rues for credit scoring using evoutionary agorithms, European Journa of Operationa Research, vo.77, no., 27, pp [] B.Y. Tsui, Microwave Recervers With Eectronic Warfare Appications. New York: Wiey, 986. [2] O. Cordón, M.J. de Jesus, and F. Herrera, A proposa on reasoning methods in fuzzy rue-based cassification systems, Internationa Journa of Approximate Reasoning, vo.2, no., 999, pp [] T. Murata, H. Ishibuchi, and M. Gen, Adusting fuzzy partitions by genetic agorithms and htograms for pattern cassification probems, Evoutionary Computation Proceedings, 998, pp [4] C. S. Shieh, and C. T. Lin, A vector neura network for emitter identification, IEEE Transactions on Antennas and Propagations, vo.5, no.8, 22, pp [5] H. J. Liu, Z. Liu, W. L. Jiang, and Y. Y. Zhou, Approach based on combination of vector neura networks for emitter identification, IET Signa Processing, vo.4, no.2, 2, pp [6] J. Cano, F. Herrera, M. Lozano, Evoutionary stratified training set seection for extracting cassification rues with trade-off precion interpretabiity, Data and Knowedge Engineering, vo.6, no., 27, pp