extfieldsofstudy:
Physics
Computer Science

text:
Research of the Inspection Optimization Strategy for Distribution Network Based on Comprehensive Information Model

To improve the quality and efficiency of inspection tasks, this paper studies the path planning optimization strategy for distribution equipment inspection of distribution networks. The comprehensive information model of each type of distribution equipment to be inspected is established by integrating the real-time monitoring information, geographic information and historic information effectively. The inspection path optimization model with an admissible cost function is established and solved by using the heuristic search A* algorithm. Comparison of the results of several inspection path planning strategies are provided to verify the effectiveness of the proposed strategy.

Introduction
The inspection of distribution devices plays an important role in detecting equipment defects and failures in time, evaluating the status of a distribution network and improving the reliability and quality of power supply [1,2]. Traditionally, the inspection path of several distribution devices involved in an inspection task is planned by the inspection crew based on their familiarity with the status and geographical locations of feeder lines and distribution equipment, which may be rewarded by inadequate and low efficient inspection for great randomness and subjectivity [3][4][5].
In order to tackle out this difficult task, many researchers have begun to study the inspection planning strategy for distribution devices by exploring recent theoretical and technical achievements in the field of Internet of Things (IoT) and big data [6,7]. Reference [8] has proposed an intelligent inspection strategy for 10-kV power lines by introducing fuzzy clustering analysis method. Starting from the actual situation and daily inspection issues of distribution networks, reference [9] developed an intelligent inspection system by effectively integrating several information systems including GIS (Geographical Information System), GPS (Global Positioning System), SCADA (Supervisory Control and Data Acquisition) and GPRS (General Packet Radio Service). However, the optimization of the inspection path has not been fully considered in current researches.
Currently, path planning technology has emerged to be a promising research issue in the field of logistics [10,11]. The development of optimal operation and maintenance strategy for unattended EMCEME 2019 IOP Conf. Series: Materials Science and Engineering 782 (2020) 032067 IOP Publishing doi:10.1088/1757-899X/782/3/032067 2 substation has been modeled as vehicle routing problem (VRP) in [12]. Reference [13] analyzed the laws of several factors in governing the performance of inspection schemes. The problem of inspection planning of a medium voltage distribution network has been formulated as an inspection path optimization model that was solved by genetic algorithm. Unfortunately, the practicalities of these strategies are not satisfying since that information on the current status of distribution equipment are usually not incorporated in their model formulation.
This paper presents a novel inspection path optimization strategy with the aim to improve the quality and efficiency of inspection tasks of distribution networks. The major innovation of this paper is as follows: 1) the established comprehensive information model can effectively integrate the real-time monitoring information, geographic information and historic information of the devices to be inspected, thereby overwhelming current path planning methods that only consider the geographic information of the inspection task; 2) a cost function that satisfies the acceptable condition of A* algorithm is formulated elaborately, thus facilitating the searching of the optimal path when employing the A* algorithm.
The remainder of this paper is structured as follow: Section 2 presents the comprehensive information models of several types of distribution devices. The path optimization model for distribution equipment inspection is formulated in Section 3, and the solution based on heuristic search A* algorithm is also presented in this section. Simulation results verifying the effectiveness of the proposed method are provided in Section 4. Finally in Section 5, the main findings of the paper are summarized.

Comprehensive information model of distribution devices
The wide application and rapid development of cross-discipline technology including IoT, GPS and GIS system, mobile communication and intelligent terminal devices provide us a better opportunity to access to more accurate and timely information of distribution devices. Accordingly, we utilize the real-time monitoring information and geographic information along with the historic information to construct a comprehensive information model of a distribution device, which is the foundation in developing our inspection path optimization strategy.

Historical Information Model
Historical Information reflect the historical operation status of a distribution device including service time, historical defect and failure, maintenance and test result and so on.
In this paper, we use an index H b called equipment historical health to represent the historical status of a distribution device. The value of H b ranges from 0 to 100 and has a positive correlation with the historical status of the equipment, i.e., a lower value of H b means a poorer operation status of an equipment, and in turn a greater probability of failure.
Normally, the failure rate of a distribution device over its lifetime can be expressed in a form of Weibull distribution as: where  is the exponential coefficients and =0.5 is preferred in this paper; t 1 and t 2 is respectively the commissioning and retire time of the distribution device, which can be obtained from the statistic In addition to the factors related to the equipment itself, meteorology factors such as wind and thunderstorm, and the environment in which the equipment locates also have a great influence on the failure rate. Considering this fact, the H b of a distribution equipment can be theoretically calculated by: Where K D is a coefficient reflecting the influence of a historic defect on the health condition of the equipment, and for an equipment without defect, K D =1, otherwise K D =0.95. Coefficient K E is used to represent the comprehensive impacts of multiple external factors on the operation status of the equipment. In this paper, K E is the average failure number of the equipment during the same period of time as the inspection to be performed over the past five years.

Real-Time State Model
The real-time operation state of a distribution equipment is also closely related to the probability of failure occurrence [15,16]. We use an index H c called real-time health to reflect the real-time status of a distribution device, and similarly, the value of H c is in the range of 0-100 and it is positively correlated with the current status of the equipment. H c is calculated by: The specific scoring method can refer to relevant specifications, e.g. Q/GDW 645-2011 "Distribution network equipment status evaluation guidelines" promulgated by the State Grid of China. The state information of each component of a distribution equipment can be obtained by means of on-line monitoring and mobile inspection, and the health index of an element can be determined by: Where M p and m p is respectively the health index and base score of component p of an equipment; K F is the component defect coefficient, and for defect-free component, Therefore, the health index H c of a distribution equipment is the weighted sum of the health indexes of its components, that is: Where M p and K p is respectively the health index and the weight coefficient of component p, and n is the total number of the components

Geographic Information Model
The geographic information of a distribution network is mainly composed of the spatial positioning data of its equipment, specifically, the geographical location information of substations, transformers, circuit breakers, isolation switches, poles, feeder lines, electricity consumers and so on, represented by geographical coordinates in a geographical map [17]. Combined with real-time traffic map, the geographic relation between the starting point of an inspection task and all the devices to be inspected can be expressed by a geographical distance matrix D n+1 as: 12 1 ( 1)   21  1 ( 1) Where d ij represents the shortest vehicle travel distance between device i and j, and d ij =∞ if there is no inspection pathway between these two devices. We use subscript '1' to represent the inspection starting point.

Optimization goal and basic assumptions
Taking the distribution network shown in Figure 1. As an example, the optimization of the inspection strategy of this distribution network is to find a path that starts from the operation and maintenance base Ⓑ and can traverse all the equipment including distribution transformer Ⓣ, ring cabinet/switchgear Ⓢ, cable Ⓒ and overhead line Ⓛ, and at the same time minimizes the cost involved in the inspection task. Traditional inspection path planning is highly dependent on the experience of inspection staff. Obviously, this way is of great randomness and subjectivity since that real time status of the equipment and real time traffic condition are not fully considered. To overcome this shortcoming, we proposes a path optimization strategy for distribution network inspection, and the principle of the method is shown in Figure 2.  The task analysis module determines the set of equipment and area of distribution network to be inspected by parsing the assigned inspection task. While the path optimization strategy indicates the optimal path for inspection according to the comprehensive information models of the equipment involved in the task.
We take following basic assumptions in formally formulate our inspection path optimization model: 1) There is only one operation and maintenance base, and it should be both the starting and ending point of an inspection path; 2) The inspection task is assigned by a superior such as the distribution network operator, and the information of the equipment to be inspected are known ahead; 3) Cable and overhead line segment to be inspected is also treated as a point in a path, and its distance to other equipment is determined on the basis of the segment ending point; 4) For two (or more) connected devices, for example a switch cabinet and the line segment it connects to, they are treated as one equivalent device of which the health index is the smaller one of the connected devices; 5) Abnormal traffic conditions such a congestions and roadwork are not considered.

Path optimization strategy
We employ the heuristic search A* algorithm to solve the path optimization model. This algorithm, after several years of development and improvement, is recognized as the most effective algorithm in solving the problem of optimal path searching [18][19][20]. The core idea of A* algorithm is to evaluate the costs of the routes from nodes to be expanded to the target node, and then give preference to route with the lowest cost to decrease the number of the nodes to expand, thereby reducing the complexity of the algorithm. For a node v m , its cost function f (m) is usually defined as: Where g (m) is the cost associated with the travelling from source node to node v m , and h (m) is the cost associated with the travelling from node v m to the target node.
The admissible condition for A* algorithm is: Where h′ (m) is the actual cost spent in travelling form node v m to the destination node. It has been proven mathematically [18] that if the admissible condition (8) are satisfied for all the evaluated costs h (m), then the searching result of the A* algorithm is admissible, namely, the obtained path is the optimal solution that has the lowest cost.
Considering the historic information, real time status and geographic information of a distribution equipment, we propose a concept of "inspection cost" to design the cost function of the path optimization model. The inspection cost associated with the path between the maintenance base and n equipment to be inspected can be expressed as: 12 1 1 21 1 ( 1) Where: c ij is inspection cost associated with the path from equipment i to j. H bj and H cj is respectively the historical health index and real-time health index of equipment j. ω b and ω c is the weighting the historical information and real-time status, where ω b +ω c =1.
We can learn from formula (10) that, a device with smaller values of H bj and H cj (i.e. worse historical and real-time status) and shorter geographic distances to the devices that have been inspected is more likely to be expanded in the inspection path.
In order to satisfy the acceptable condition of A* algorithm, we construct a cost function for a certain inspection path as: Where m is index of the last inspected device; C(1,m) is the total inspection cost associated with the route from the inspection base to equipment m along the examined path; (n+1-m) indicates the number of remaining routes; min c is the minimum value of all inspection costs with non-zero values. Obviously, h (m) in formula (10) satisfies the admissible condition formula (8). Figure 3. Illustrates the implementation of our inspection path optimization strategy based on A* algorithm.

Simulation model
We consider the inspection task of a distribution network shown in Figure 4. This task involves the inspection of eight distribution devices dispersedly located in the network. The distance between two adjacent devices is marked beside the corresponding route. The proposed path optimization strategy is coded in MATLAB software.    Table 2 lists the health indices of each device, and we can learn that equipment 5 is the one with the highest operation risk since that it's H c is only 60.  2  90  90  3  98  95  4  90  95  5  95  60  6  86  80  7  90  85  8  95  90  9 99 98

Path planning result comparison
The path planning result of our strategy (strategy 3) is compared with those of two traditional methods (strategy 1 and 2). Strategy 1: Path planning based on human experience. In this method, the inspection staff tend to choose the device that has the shortest distance from their current position as the next one to be inspected. Thus for the inspection task shown in Fig.4, the final inspection path is [1-9-8-7-6-5-4-3-2-1], and the total inspection distance is 32.8km. Strategy 2: Path planning based on device real time status. The principle of this method is to give higher inspection priority to devices with a lower value of health index H c . According to Table 2, the final result of this strategy is the path [1-5-6-7-8-9-2-3-4-1], and the total inspection distance is 35.4km. Strategy 3: Path planning based on comprehensive information model. Figure 5. Shows the inspection cost of two adjacent devices for ω b =0.2 and ω c =0.8. By using our proposed inspection path optimization strategy, the optimal path is [1-5-6-4-3-2-9-8-7-1], and the total inspection distance is 30km. Table 3 summarizes the results of the three path planning methods. We can learn from Table 3 that the inspection path for our strategy is of the shortest total distance of 30km, which saves 9.33% and 18% of the inspection cost, as compared with strategy 1 and 2. Meanwhile, distribution device 5, which is of the worst health condition, is the first equipment to be inspected for our strategy and strategy 2, thus effectively tackling out the problems of randomness and subjectivity of strategy 1 in planning the inspection path.
These simulation results prove that our strategy can effectively incorporate different types of information of the devices into the inspection path planning, and it has better comprehensive performances in term of inspection quality and efficiency.

Conclusion
This paper presents a novel strategy to optimize the inspection path in fulfilling inspection tasks of distribution networks. Comprehensive information models of different kinds of distribution equipment are developed to incorporate the real-time monitoring information, geographic information and historic information of the devices to be inspected into the inspection path optimization. The path optimization model with a special designed cost function is solved by using the heuristic search A* algorithm. Simulation results prove that the proposed strategy can tackling out the problems of randomness and subjectivity of current inspection strategy and at the same time improve the inspection efficiency.


s2fieldsofstudy:
Business
Environmental Science

text:
Aerodynamic Optimization of Airborne Radome for Maritime Patrol Radar

Airborne Early Warning (AEW) systems are deployed for getting surveillance information on airborne enemy targets. Electromagnetic sensors such as Radars are integrated on airborne platforms for collecting such information. Maritime Patrol Radar (MPR) is used for surveillance of sea surface for various types of ships and low flying aircraft. The antenna of MPR is belly mounted on typical turbo prop aircraft and protected from environment with a cover called Radome. Airborne radomes are electromagnetically transparent. The radome installation introduces additional drag which will reduce the range of the aircraft. To minimise the drag due to installation of radome, the profile has to be stream-lined or optimised with CFD analysis for certain operational points of aircraft flight. Design of radome is multidisciplinary effort involving Aerodynamics, Structures and Electromagnetic disciplines. In this study, aerodynamic optimization of a radome for a given antenna size is carried out using a combination Genetic Algorithm (GA) and traditional optimisation methods to find the Utopia point for further investigation on Multidisciplinary Design Optimization (MDO) of radome. This is necessary to progress on optimisation with other disciplines like Structures and Electromagnetics (EM)

I. INTRODUCTION
Airborne Early Warning (AEW) systems are used for airborne surveillance to get advance information on the incoming enemy fighters or targets. RADAR is electromagnetic system which is integrated on suitable airborne platform such as executive jets or turbo-prop aircraft for carrying out airborne surveillance and early warning. Maritime Patrol Radar (MPR) is such a radar which provides surveillance information on the targets which are flying low above the sea surface or enemy ships sailing on the seas. As part of MPR system, an antenna is installed below the fuselage to transmit / receive Electro-Magnetic (EM) signals. A typical installation of MPR Radome is illustrated in Fig. 1. To protect an antenna from environmental conditions like, rain, sandstorm, hail etc., a cover is required. This cover is termed radome and is electromagnetically transparent. It has to offer least resistance to electromagnetic signals transmitted/received and at the same time structurally strong enough to withstand air loads and other environmental effects [1].  In this paper, an approach for the optimization of the shape the airborne radome from aerodynamic performance is presented as a part of the larger study on Multidisciplinary Design Optimization (MDO) of the radome.

II. REVIEW OF LITERATURE
Effect of drag on the shape and location of airborne radome is studied by Girgosian P et al [2]. It is evident that the location and the length to height ratio of radome have large effect on the radome drag. Other parameters that have significant effect are radome's wetted area, width and subtended angle at the tail portion. Effect on radome sizing and location on the drag have been studied for various configurations and reported. Satellite Communication (SATCOM) radomes used for land, shipboard, or airborne applications should protect the antenna system from environmental conditions like rain, winds, ice, saline environment etc. Also the physical impact of the sea waves has to be accounted for radomes in maritime environment. A multi objective optimization approach with electrical and mechanical design considering cost also is suggested by O Russo et al [3]. Authors have used a sequential approach in selection of radome materials, analyses for electrical and mechanical properties, multiobjective optimization for composite layup design, experimental verification on samples and full scale testing of the final products. In the present work, a mathematical model is evolved which can integrate various disciplines and carry out multi-disciplinary optimization. Toivanen, J. et al [4], have studied optimization of an airfoil shape involving aerodynamics and electromagnetics. The drag coefficient and strength of backscattered radiation (RCS) of an airfoil are minimized in a multi-objective optimization problem setup. Drag computation is based on Euler equations. Makinen, R. A. E. et al [5] studied the above problem by employing Navier Stokes equations solver for CFD and same Helmholtz equation for CEM.

Renuka.
A. et al [6] have discussed the design aspects of dielectric airborne radomes. It is highlighted that the design of radome is generally driven by aerodynamic considerations. Slotted waveguide antenna pattern with and without the radome is analysed using a software based on physical optics method. The output of the software is the estimate of bore sight error with respect to scan angles. In multi-objective optimization, there are several methods to attach priority to the objectives. Marler. et al [7] discussed about two broad approaches for assignment of weights for the objectives, namely, ranking and rating approach. The importance and role of weights in MDO are brought out and it is informed that the weights represent the change in preference function of objectives. Lee. K. W. et al [8] proposed a simple design equation for A-sandwich radome design for aircrafts, missiles as well as fixed ground installations. Radomes are proposed as thin or multiple half-wavelengths (λ/2). Radomes with good EM transmission properties are with the thickness of λ/20. This radome will not be able to sustain harsh environmental conditions and is structurally weak. Half-wavelength radomes are sturdy but have very narrow band characteristics. Hence a sandwich panel with two skins (one on either side) of λ/20 thickness and a core of λ/2 thickness has good mechanical strength as well as good transmission characteristics. This paper arrives at the empirical formulae to arrive at the skin thickness (d) and core thickness based on the operational frequency. These compare well with some experimental results.

III. AIRBORNE RADOMES
RADOME (RADar Dome) is a cover that gives environmental protection to the Radar Antenna. Radomes can be of monolithic or sandwich construction according to the type of construction. Since the radomes have to be electromagnetically transparent, dielectric materials such as Glass fibre and Aramid fibre are used for construction of radomes. According to dielectric wall construction, different styles of radomes are defined, which are namely thin walled, half wavelength, A-Sandwich, B-Sandwich and C-Sandwich and multi-layered [1]. Fig. 2 shows typical radome styles. A-Sandwich and C-Sandwich radomes are widely used in aircraft. Since softer core is present on either side in B-Sandwich it is not generally used. Radomes are also classified as Constant Thickness (CT) and Variable Thickness (VT) radomes.

Figure 2. Airborne Radome Classification [1]
For the design of radomes, typically E-Glass or Quartz is used for composite skins (layers). Quartz offers lowest EM signal loss in Glass fibres and hence it is often preferred. Non-metallic Honeycombs and many types of foams are used as cores in Sandwich constructions.

IV. RADOME DESIGN-MULTIDISCIPLINARY EFFORT
Any external installation of a structure on the fuselage of an aircraft offers resistance to air flow during its flight thereby increasing the drag. The drag has an undesired effect of reducing aircraft range and its speed. As radome is a necessity to protect the antenna from environment, it is imperative that the effect of its installation, i.e., drag, has to be reduced as much as possible. Radome design is a multidisciplinary design effort involving structural, aerodynamic and electromagnetic disciplines. The design requirements for each of these disciplines could be contradictory in nature. For the structures, the radome needs to be thin and as small as possible to be least in weight. For aerodynamics, to have least drag, the structure has to be streamlined and slender. For least losses in terms of electromagnetics, the radome has to be thinner and flatter. Hence radome design is dependent on the materials used (strength characteristics), its size (length, width and height), radome thickness, type of construction (monolithic or sandwich) and shape. Each of these parameters or variables affect (a) Weight of the radome (b) External disturbance it will cause in flight i.e., drag and (c) Electromagnetic losses such as Radar Transmission Efficiency (RTE) and Insertion Phase Delay (IPD) Given the choice of material, i.e., Glass Fibre and Honeycomb, the design variables in the design of radome are its shape (function of its profile), size and thickness.
V. Optimization Problem Statement The optimization problem of radome can be expressed as Minimise where F is the objective function to be minimised and is itself a function of J 1 (drag), J 2 (weight) and J 3 (EM loss). This is a MDO problem with more than one objective to be optimised. It involves multidisciplinary analyses i.e., Structural, Aerodynamics and Electromagnetics which need to be integrated to interact with each other. Each of these disciplines is required to evaluate the objective functions and the combination of three objectives from three disciplines is to be minimised. The optimization function is obtained from Eqn. 1 as below where are weights assigned to each disciplinary objective. Various schemes for assigning weights have been reviewed by Marler [7]. Normalization of the objectives is discussed and methods to normalize the function before assigning weights are elaborated.
A Utopia point is a point in the design space where all the objectives are simultaneously at their optimum; however, this is not achievable in reality. Knowledge of the Utopia point is a requirement for most of the schemes where weights are to be assigned to the objectives. The optimum points when each of these objectives is considered in isolation is to be determined to arrive at the weights and scheme for implementation of weights to be attached to each of the objectives while handling Multi-objective problem. In this study the design is presented where the optimum (minimum) objective is the drag.

VI. RADOME SHAPE AND ITS AERODYNAMIC EFFECT
Radomes are generally axisymmetric about the longitudinal axis of the aircraft. Three-Dimensional (3D) shape of the radome is derived from a 2D spline which is defined on XY plane of aircraft. Fig. 3 shows typical 2D spline which defines the radome cross section. When this 2D spline is revolved 180 0 about longitudinal axis, radome's 3D shape is obtained. Radome shape determines the drag for a given size of radome and for a given flight condition. With the 3D shape of the radome determined, thickness can be added to radome. Different layers of laminates of the radome and the core thickness can then be defined as part the overall thickness of radome. For the present study, Constant thickness (CT) radome with A-Sandwich construction is considered.

Figure 3. Typical Radome Cross Section
The radome has to have a minimum volume at least equal to that of the antenna it needs to house. An antenna is installed inside the radome and it is rotated 360 0 about its axis in the azimuth for sending and receiving EM signals. Hence a minimum swept volume created by rotating a flat plate about an axis perpendicular to longitudinal axis, i.e., a cylinder with a minimum diameter and height needs to be housed in the radome. This cylinder defines the lower limits for the height and width of the radome at the location where the antenna has to be installed. Fig. 4 shows the radome 3D shape and minimum swept volume required for installation of antenna inside the radome.  (6) where J(x) is Drag due to radome and x is vector of design variables (as given in Table 1). Aim of the optimization study is to arrive at a radome shape for which the drag experienced is minimum, at the selected operational point of the maritime aircraft. This has to be achieved by estimating drag for various radome profiles and mathematically choosing the shape for which the drag is near minimum.
For studying radomes of different lengths and contours, the profile of radome is varied by varying the X and Y coordinates of various control points or Design Variables (DV) (see Fig. 5) within lower and upper bounds (as in Table 1).

Figure 5. Variation of control points of radome
In Fig. 5, points 1 to 11 are the control points which determine the cross section of the radome under study. Point 0 is fixed at 0,0 (origin) and the point 12 is fixed at L,0 where L is the length of the radome. All the X coordinates (i.e., horizontal distance from point 0) are varied as a percentage of total length "L". The Y coordinates of each of these control points is varied within the upper and lower bounds (see Table 1). All the dimensions are in "metres".

B. CFD analysis
Drag of a chosen radome shape needs to be estimated using CFD simulation in ANSYS. To start with, profile (2D) of radome is modelled with initial values of the control points and a spline is created by joining these points. The 3D shape is then created by revolving the 2D spline 180 deg about X axis, as explained in section VI. The control points (design variables) are defined as parameters in ANSYS so that these can be imported into optimization software for defining upper and lower bounds (side constraints). The optimization software will vary the values of the design variables based on the values of the objective (drag) at each of the iterations. The flow domain is modelled and CFD mesh is created with using tetrahedral mesh and prism layers. Parameters of the CFD mesh are given Table 2. The parameters of CFD mesh are arrived at after a convergence analysis for initial geometry. To capture the boundary layer effect, prism layers are created adjacent to radome wall. CFD mesh and the prism layers are shown in Fig. 6 and Fig. 7 respectively. The initial and boundary conditions are defined for the flow analysis. The mesh gets automatically resized in ANSYS software based on the changed geometry points fed by the optimization software. Some analysis runs had returned zero value of drag since the mesh resizing had failed in those cases.

C. Optimization Process
The optimization process is carried out by optimization software modeFrontier. For carrying out the optimization, the inputs (design variables) and output (drag) of the CFD software are linked to the optimizer algorithm. The process is briefly explained in Fig. 8. The optimizer creates a design table (step 1), i.e., combination of different values of design variables. The optimiser invokes ANSYS Workbench in batch mode and passes on the initial values of design variables (step 2). These design variables which are defined as parameters in ANSYS are used to create new profile of radome (step 3). ANSYS software then runs flow simulation using Fluent code (step 4) and determines the drag value (step 5) for the current shape of the radome. This drag value is read by modeFrontier to evaluate the objective function (step 6). Based on the value of objective function, new set of values for the design variables are determined (step 8) by the optimiser algorithm and the same is again sent for carrying out CFD simulation. The steps 3 to 8 are repeated in a loop. Exiting the loop (step 7) is based on the stop criterion which explained in following paragraphs.
An adaptive multi strategy optimization algorithm called pilOPT is used to carry out the optimization. Depending on number of design variables, number of objective function or functions, and the time for each iteration, the algorithm adopts design space exploration and optimization strategy such as Response Surface Model based optimization, Genetic algorithms, Evolution strategy, Particle swarm intelligence, simulated annealing, game theory, gradient based methods to find the direction of search and the minima. In general terms, the design space is initially explored with Genetic Algorithm (GA) to fully explore the design space in order to find out the extent of impact of the design variables on the objective function. Gradient based approach is then used to localise and find the optimum value of objective function based on the gradient information of objective function.
The absolute minimum is generally never reached in such a problem and hence the stop criterion is number of iterations. Additionally, the operation loop terminates if the improvement in objective function in successive iterations is less than a prescribed value. In an autonomous mode the algorithm stops further evaluation when the Pareto front does not improve further for multi-objectives problem.

Figure 8. Steps in Optimization Process
The control points are varied within the upper and lower limits so as to explore different shapes of the radome. When the value for adjacent control points are varied within the limits, it ends up in wavy shapes and smooth shapes as well.
The objective (drag) is evaluated and the optimiser drives towards the profile having lesser drag values. Some profiles generated by optimizer and evaluated by the CFD software are depicted in Fig. 9. In this it is clear that the optimizer has explored the design space thoroughly and generated different profiles for various lengths of the radome. The natural selection is towards most streamlined profiles which give lower values of drag. Around 800 iterations (profiles) are generated and evaluated by optimizer to arrive at the profile with minimum drag.

VII. RESULTS AND DISCUSSION
In the initial stages, the optimiser tries to evaluate designs to the full extent of the design space, i.e., it tries to explore the whole design space which is defined by the limits for all design variables. Based on initial evaluations and the value of objective (drag) of these designs, optimiser tries to localise where possible minimum values could occur. A case of how the designs of different radome profiles are explored for a length of 2.25m is shown in Fig. 10.

Figure 10. Optimization progress for 2.25m length radome
Initially more designs with varying drag values are evaluated with uneven profiles also being included for design exploration (case of 153N). Later profiles become smoother (case of 57.5N) and get further streamlined (case of 34N). Similar trend is seen in all the radome lengths explored from 1.5m to 3.0m.
Progress of optimisation of all length cases is shown in Fig.  11. Here, up to around 100 iterations or so, radome designs evaluated have drag values from as low as 50N to as high as 300N. As the optimisation progresses, this value narrows down and reduces to less than 50N in phased manner and gets restricted to a narrow band. The radome profiles get more streamlined as is evident with lower values of objective values with the progress of optimization. The optimizer process terminates when the reduction in the drag values become lesser and lesser. The optimization process took nearly 36 hours for completion. Figure 11. Trend of objective values Fig. 12 shows the initial profile, the radome profiles which have highest (worst) drag value and the least (best) drag values. Due to unevenness in the profile, the drag is high for this profile. This is one of the designs evaluated initially. Among the designs evaluated, the highest drag value is 279N for a radome of 1.5m length. The best profile is fully streamlined and hence the drag values drops down to 33.5N.
Further continuation of optimization does not result in much reduction in this value and hence it can be terminated.

Figure 12. Initial, worst and best radome profiles
Drag value is the sum the of pressure (form) drag and skin friction drag as computed by CFD software. Pressure drag depends on the form of radome and skin friction drag depends on its length, which is again a trade-off. Longer stream lined radomes will have less form drag but skin friction drag will be more. Shorter radomes will have less skin friction due to lower wetted area but have higher form drag due to higher pressure gradients. Optimized radome is shown in Fig. 13. Length of this radome is 2.48m and drag value of this radome is 33.5 N.

VIII. CONCLUSIONS
In this study, aerodynamic optimization is performed using ANSYS and modeFrontier optimization software by varying radome lengths and the profiles while ensuring antenna of known size can be accommodated inside the radome. The results indicate that the sleeker profile (lower l/d ratios) provide lesser drag values. The best profile in terms of least drag is established using optimisation algorithms, which is subject to lower and upper bounds for design variables and constraints. Present study considered aerodynamic aspects of the radome design and evaluated best design with respect to this single discipline and Utopia point with respect to aerodynamics is found. The structural and EM aspects of the radome are to be integrated to carry out multi-objective MDO analysis and optimization. The Utopia points with respect to structures and EM also needs to be explored.