Effectiveness Evaluation of Air and Missile Defense System Based on Parametric Diagrams

Abstract

Under the complex operational environment of the antimissile operation, the application of Systems Modeling Language (SysML) parametric model in weapon system effectiveness evaluation is explored. The function of parametric graph model, the construction process of the model and the optimization method of the model are researched. Using feedback mechanism to collect, collate and calculate the parameters of the model, and realize the leap from the index relationship description to the calculation of the index. Finally, the feasibility and effectiveness of the proposed method is verified by using the system of antimissile weapon system as an example. Introduction With the rapid development of space technology and the continuous development of missile technology and under the high-tech war background, using missiles to destroy critical operational facilities has become an important form of combat. In order to achieve victory in the war in the future, to prevent our own key objectives be destroyed causing a rapid decline in the combat effectiveness, we must intercept and destroy the enemy missiles in launch process. The core features of antimissile operations is scout and pre-alarming integration, command and control command integration and comprehensive fire application. As a new type of cutting-edge technology application, it is necessary to make a scientific demonstration before the construction of air and missile defense weapon system. In American industry the definition of system effectiveness is: a function of the reliability and validity of the system and the degree of completing a set of tasks. The analysis and evaluation of the effectiveness of the air and missile defense system has important significance for the deployment, evaluation, development and optimization of anti missile weapon system. parametric diagram model SysML is a new system engineering standard modeling language proposed by the International Council on Systems Engineering (INCOSE) and The object management organization(OMG) based on the reuse and extension of UML2.0. Fig.1 SysML structure view 5th International Conference on Computer Sciences and Automation Engineering (ICCSAE 2015) © 2016. The authors Published by Atlantis Press 847 SysML defines nine types graphics to visualize a systems engineering model, as shown in Fig. 1. Parametric graph is a unique view model of SysML, which is based on the existence of object attributes and the relationship between the attributes of each object in the system. The parametric graph ordinary use to directing relationship between object attributes in order to analyze the function, measure the effectiveness and clarify the relationship among the variables. Construction of parametric diagram model Parametric diagram represents the relationship between the attributes of each object in the system, which determines that the argument graph is not an isolated existence, but rather the relationship between them. In IBM Rational Rhapsody modening tool the graphical elements used by the parameter diagram are called constraint block, and these models are defined by general or basic mathematical formulas. The purpose of parametric drawing is to analyze the key parameters of system, including performance evaluation, reliability evaluation and physical property evaluation. Evaluation is an indispensable part of the system engineering process, UML and IDEF modeling language has no parameter diagram, so they can't carry out engineering analysis. In the previous modeling language, there is no standardization of engineering analysis model, this leads to the failure to associate the system static structure model and the structure behavior of the system and leads to serious mismatch between structure and behavior. Furthermor, system structure model and engineering analysis model can't be unified and synchronized design, these increase the complexity and dissimilarity of the system, so the analysis model has to be constructed independently in the engineering analysis. This traditional approach lead to the increase in the number of engineering analysis models and easy to appear the structure model and the behavior model inconsistent phenomenon. In the process of system internal structure modeling in Rhapsody, parametric diagram model describes what attributes the system has and what is the relationship between these attributes. The constraint relations in parametric model are expressed by equation, the parameters in the equation are the system attributes and the equation itself describes the constraint relationship of the attributes. When building parametric diagram, parameter attributes in constrained blocks are derived from the properties of the parameters in the block diagram. in the parameter model and the attributes in the block diagram are actually placed in different places of the same object, They are related to each other. The parameters of the other parts are changed as the parameters are modified. Such mechanisms ensure the consistency of the relationship between the parameters and the parameters value in the whole process of the system modeling. By establishing system parametric diagram model, it can clearly reflect the relationship between the properties of the system and the properties of the system parameters. When the performance parameters of the system are analyzed, the performance and efficiency of the system can be quantitatively analyzed. constraintproperty_0 1 > C onstraints T=T1+T2+T_Fire+T_Desicion+T_Plan T1 > Constraints T1=I1/C C I1 T2 > Constraints T2=I2/C I2 C Fig.2 A simple parameter diagram 848 Fig.2 shows a simple parameter diagram.The boxes Attributes represent the attributes parameter of system, the boxes ConstraintBlock represent the constraints of parameters,which represents the constraint equations between attributes. In Fig.2, the constraint equation of the constraint equation is T1=I1/C, that is, the value of and I1 can be calculated by T1 and C. According to the constraint equation can calculate the value of the target attribute or the optimal value of the target attribute according to the constraint relationship. Construction and analysis of effectiveness evaluation model of air and missile defense model based on parametric diagram In this paper, We use parametric diagram model to evaluate the effectiveness of high-level terminal interception phase and calculate the successful probability of intercepting an enemy incoming missile. As shown in Fig.3, the parameter block definition diagram describes the performance parameters of the key equipment in the antimissile equipment system, which includes the constraint relationship between the parameters of each module and the type and property of the system. As shown in Fig.3, in the parameter block WarningRadar, we calculate the probability of discovering targets (Pd). Use some performance parameters of early warning radar such as target echo power(Snr), noise power(S) and minimal signal-to-noise ratio reliability( Npr). Through the calculation of the corresponding constraint formula in the block, the probability of the early warning radar to discover the target is eventually obtained. The constraint formula is as form (1): exp( ( /(1 ( / )))) d pr P Snr S N    (1) The Energy Test Equipment parameter block is defined under the parameter block WarningRadar to calculate noise power. The constraint formula is as follows: pr nr p b N B B N R     (2) In the form (2), Npr express noise power, B express Boltzmann constant, 1.38 10 ^ ( 23) B    J/k。 nr B express reference noise figure, p N express noise figure, b R express receiver bandwidth. The purpose of Defence Missile is calculate missile destroy probability k P . L express missile killing radius, G express guidance accuracy. The constraint formula is as follows: / k P L G  (3) Finally, we use Air Defence System parameter block to calculate the successful probability of intercepting an enemy incoming missile (Ps). The constraint formula is as follows: / s d k P P P  (4) WarningRader > ConstraintParameters Npr Pd S SNR Snr Constraints {{Pd} Pd=exp(-Snr/(1+SNR))} {{SNR} SNR=S/Npr} 1 AirDefenceSystem > ConstraintParameters Pd Pk Ps Constraints {{Ps} Ps=Pd*Pk} DefenseMissile > ConstraintParameters G L Pk Constraints {{Pk} Pk=L/G} 1 EnergyTestEquipment > ConstraintParameters B Bnr Np Npr Rb Constraints {{Npr} Npr=B*Bnr*Np*Rb} 1 Fig.3 Parameter block definition diagram